LMFDB - Embedded newform 63.2.s.b.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(47,63)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("63.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.3
Root			$-0.539982 + 0.935277i$ of defining polynomial
Character	$\chi$	$=$	63.47
Dual form			63.2.s.b.59.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.254498 + 0.146935i) q^{2} +(-1.27564 + 1.17164i) q^{3} +(-0.956820 + 1.65726i) q^{4} +3.06027 q^{5} +(0.152492 - 0.485617i) q^{6} +(-1.22581 + 2.34465i) q^{7} -1.15010i q^{8} +(0.254498 - 2.98919i) q^{9} +O(q^{10})$	\(q+(-0.254498 + 0.146935i) q^{2} +(-1.27564 + 1.17164i) q^{3} +(-0.956820 + 1.65726i) q^{4} +3.06027 q^{5} +(0.152492 - 0.485617i) q^{6} +(-1.22581 + 2.34465i) q^{7} -1.15010i q^{8} +(0.254498 - 2.98919i) q^{9} +(-0.778834 + 0.449660i) q^{10} -3.89647i q^{11} +(-0.721166 - 3.23512i) q^{12} +(2.02935 - 1.17164i) q^{13} +(-0.0325450 - 0.776824i) q^{14} +(-3.90379 + 3.58555i) q^{15} +(-1.74465 - 3.02182i) q^{16} +(1.68263 + 2.91440i) q^{17} +(0.374446 + 0.798138i) q^{18} +(2.20696 + 1.27419i) q^{19} +(-2.92813 + 5.07167i) q^{20} +(-1.18341 - 4.42714i) q^{21} +(0.572527 + 0.991647i) q^{22} -2.98075i q^{23} +(1.34751 + 1.46711i) q^{24} +4.36525 q^{25} +(-0.344311 + 0.596363i) q^{26} +(3.17762 + 4.11130i) q^{27} +(-2.71283 - 4.27489i) q^{28} +(-3.67241 - 2.12027i) q^{29} +(0.466668 - 1.48612i) q^{30} +(-0.409400 - 0.236367i) q^{31} +(2.88005 + 1.66280i) q^{32} +(4.56528 + 4.97049i) q^{33} +(-0.856452 - 0.494473i) q^{34} +(-3.75130 + 7.17527i) q^{35} +(4.71035 + 3.28188i) q^{36} +(-3.89395 + 6.74451i) q^{37} -0.748891 q^{38} +(-1.21596 + 3.87227i) q^{39} -3.51962i q^{40} +(-3.12737 - 5.41676i) q^{41} +(0.951677 + 0.952814i) q^{42} +(2.06191 - 3.57133i) q^{43} +(6.45748 + 3.72823i) q^{44} +(0.778834 - 9.14772i) q^{45} +(0.437976 + 0.758597i) q^{46} +(-2.02694 - 3.51076i) q^{47} +(5.76605 + 1.81064i) q^{48} +(-3.99479 - 5.74818i) q^{49} +(-1.11095 + 0.641408i) q^{50} +(-5.56106 - 1.74627i) q^{51} +4.48421i q^{52} +(-4.99439 + 2.88351i) q^{53} +(-1.41279 - 0.579416i) q^{54} -11.9243i q^{55} +(2.69658 + 1.40980i) q^{56} +(-4.30818 + 0.960372i) q^{57} +1.24616 q^{58} +(-2.34352 + 4.05910i) q^{59} +(-2.20696 - 9.90033i) q^{60} +(-1.38580 + 0.800092i) q^{61} +0.138922 q^{62} +(6.69664 + 4.26088i) q^{63} +6.00131 q^{64} +(6.21035 - 3.58555i) q^{65} +(-1.89219 - 0.594182i) q^{66} +(-0.787831 + 1.36456i) q^{67} -6.43989 q^{68} +(3.49238 + 3.80236i) q^{69} +(-0.0995964 - 2.37729i) q^{70} -13.6132i q^{71} +(-3.43786 - 0.292699i) q^{72} +(-0.856452 + 0.494473i) q^{73} -2.28862i q^{74} +(-5.56848 + 5.11453i) q^{75} +(-4.22333 + 2.43834i) q^{76} +(9.13588 + 4.77633i) q^{77} +(-0.259511 - 1.16415i) q^{78} +(4.63908 + 8.03512i) q^{79} +(-5.33910 - 9.24760i) q^{80} +(-8.87046 - 1.52149i) q^{81} +(1.59182 + 0.919038i) q^{82} +(-5.49361 + 9.51520i) q^{83} +(8.46924 + 2.27475i) q^{84} +(5.14930 + 8.91884i) q^{85} +1.21186i q^{86} +(7.16886 - 1.59807i) q^{87} -4.48133 q^{88} +(2.15849 - 3.73861i) q^{89} +(1.14591 + 2.44252i) q^{90} +(0.259511 + 6.19433i) q^{91} +(4.93989 + 2.85205i) q^{92} +(0.799185 - 0.178153i) q^{93} +(1.03171 + 0.595655i) q^{94} +(6.75390 + 3.89937i) q^{95} +(-5.62211 + 1.25327i) q^{96} +(-4.98797 - 2.87980i) q^{97} +(1.86128 + 0.875930i) q^{98} +(-11.6473 - 0.991647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7}+O(q^{10}) $ 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7	$ 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7} - 15 q^{10} + 6 q^{13} - 6 q^{14} - 3 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} + 3 q^{19} - 3 q^{20} + 18 q^{21} + 5 q^{22} + 27 q^{24} - 14 q^{25} + 3 q^{26} + 27 q^{27} + 2 q^{28} - 15 q^{29} - 9 q^{31} + 48 q^{32} - 9 q^{33} + 3 q^{34} - 15 q^{35} - 18 q^{36} + 6 q^{37} + 36 q^{38} + 12 q^{39} - 9 q^{41} - 6 q^{42} + 3 q^{43} + 24 q^{44} + 15 q^{45} - 13 q^{46} + 15 q^{47} - 15 q^{48} - 23 q^{49} + 3 q^{50} - 24 q^{51} - 9 q^{53} + 27 q^{54} - 51 q^{56} - 36 q^{57} - 16 q^{58} - 18 q^{59} - 3 q^{60} + 12 q^{61} + 12 q^{62} + 9 q^{63} + 6 q^{64} - 3 q^{65} - 33 q^{66} - 10 q^{67} - 54 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{72} + 3 q^{73} - 21 q^{75} + 9 q^{76} + 45 q^{77} + 24 q^{78} + 20 q^{79} - 30 q^{80} - 48 q^{81} + 9 q^{82} - 15 q^{83} + 60 q^{84} + 18 q^{85} + 30 q^{87} + 16 q^{88} + 24 q^{89} + 24 q^{90} - 24 q^{91} + 39 q^{92} + 6 q^{93} - 3 q^{94} + 3 q^{96} + 6 q^{97} + 45 q^{98} + 21 q^{99}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7 - 15 * q^10 + 6 * q^13 - 6 * q^14 - 3 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 + 3 * q^19 - 3 * q^20 + 18 * q^21 + 5 * q^22 + 27 * q^24 - 14 * q^25 + 3 * q^26 + 27 * q^27 + 2 * q^28 - 15 * q^29 - 9 * q^31 + 48 * q^32 - 9 * q^33 + 3 * q^34 - 15 * q^35 - 18 * q^36 + 6 * q^37 + 36 * q^38 + 12 * q^39 - 9 * q^41 - 6 * q^42 + 3 * q^43 + 24 * q^44 + 15 * q^45 - 13 * q^46 + 15 * q^47 - 15 * q^48 - 23 * q^49 + 3 * q^50 - 24 * q^51 - 9 * q^53 + 27 * q^54 - 51 * q^56 - 36 * q^57 - 16 * q^58 - 18 * q^59 - 3 * q^60 + 12 * q^61 + 12 * q^62 + 9 * q^63 + 6 * q^64 - 3 * q^65 - 33 * q^66 - 10 * q^67 - 54 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^72 + 3 * q^73 - 21 * q^75 + 9 * q^76 + 45 * q^77 + 24 * q^78 + 20 * q^79 - 30 * q^80 - 48 * q^81 + 9 * q^82 - 15 * q^83 + 60 * q^84 + 18 * q^85 + 30 * q^87 + 16 * q^88 + 24 * q^89 + 24 * q^90 - 24 * q^91 + 39 * q^92 + 6 * q^93 - 3 * q^94 + 3 * q^96 + 6 * q^97 + 45 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.254498	+	0.146935i	−0.179958	+	0.103899i	−0.587273	−	0.809389i	$-0.699798\pi$
$2$	−0.254498	+	0.146935i	−0.179958	+	0.103899i	0.407315	+	0.913288i	$0.366465\pi$
$3$	−1.27564	+	1.17164i	−0.736489	+	0.676449i
$3$	−1.27564	+	1.17164i	−0.736489	+	0.676449i
$4$	−0.956820	+	1.65726i	−0.478410	+	0.828631i
$5$	3.06027			1.36859			0.684297	−	0.729203i	$-0.260109\pi$
$5$	3.06027			1.36859			0.684297	+	0.729203i	$0.260109\pi$
$6$	0.152492	−	0.485617i	0.0622547	−	0.198252i
$7$	−1.22581	+	2.34465i	−0.463312	+	0.886195i
$7$	−1.22581	+	2.34465i	−0.463312	+	0.886195i
$8$		−	1.15010i		−	0.406622i
$9$	0.254498	−	2.98919i	0.0848328	−	0.996395i
$10$	−0.778834	+	0.449660i	−0.246289	+	0.142195i
$11$		−	3.89647i		−	1.17483i	−0.809285	−	0.587416i	$-0.800145\pi$
$11$		−	3.89647i		−	1.17483i	0.809285	−	0.587416i	$-0.199855\pi$
$12$	−0.721166	−	3.23512i	−0.208183	−	0.933898i
$13$	2.02935	−	1.17164i	0.562840	−	0.324956i	−0.191445	−	0.981503i	$-0.561317\pi$
$13$	2.02935	−	1.17164i	0.562840	−	0.324956i	0.754285	+	0.656548i	$0.227984\pi$
$14$	−0.0325450	−	0.776824i	−0.00869801	−	0.207615i
$15$	−3.90379	+	3.58555i	−1.00796	+	0.925785i
$16$	−1.74465	−	3.02182i	−0.436163	−	0.755456i
$17$	1.68263	+	2.91440i	0.408097	+	0.706845i	0.994677	−	0.103047i	$-0.0328591\pi$
$17$	1.68263	+	2.91440i	0.408097	+	0.706845i	−0.586579	+	0.809892i	$0.699526\pi$
$18$	0.374446	+	0.798138i	0.0882577	+	0.188123i
$19$	2.20696	+	1.27419i	0.506312	+	0.292319i	0.731316	−	0.682038i	$-0.238906\pi$
$19$	2.20696	+	1.27419i	0.506312	+	0.292319i	−0.225004	+	0.974358i	$0.572240\pi$
$20$	−2.92813	+	5.07167i	−0.654750	+	1.13406i
$21$	−1.18341	−	4.42714i	−0.258242	−	0.966080i
$22$	0.572527	+	0.991647i	0.122063	+	0.211420i
$23$		−	2.98075i		−	0.621530i	−0.950487	−	0.310765i	$-0.899415\pi$
$23$		−	2.98075i		−	0.621530i	0.950487	−	0.310765i	$-0.100585\pi$
$24$	1.34751	+	1.46711i	0.275059	+	0.299472i
$25$	4.36525			0.873051
$26$	−0.344311	+	0.596363i	−0.0675249	+	0.116956i
$27$	3.17762	+	4.11130i	0.611532	+	0.791219i
$28$	−2.71283	−	4.27489i	−0.512676	−	0.807879i
$29$	−3.67241	−	2.12027i	−0.681949	−	0.393724i	0.118640	−	0.992937i	$-0.462147\pi$
$29$	−3.67241	−	2.12027i	−0.681949	−	0.393724i	−0.800589	+	0.599214i	$0.795480\pi$
$30$	0.466668	−	1.48612i	0.0852015	−	0.271327i
$31$	−0.409400	−	0.236367i	−0.0735305	−	0.0424528i	0.462784	−	0.886471i	$-0.346851\pi$
$31$	−0.409400	−	0.236367i	−0.0735305	−	0.0424528i	−0.536314	+	0.844018i	$0.680184\pi$
$32$	2.88005	+	1.66280i	0.509126	+	0.293944i
$33$	4.56528	+	4.97049i	0.794714	+	0.865251i
$34$	−0.856452	−	0.494473i	−0.146880	−	0.0848014i
$35$	−3.75130	+	7.17527i	−0.634086	+	1.21284i
$36$	4.71035	+	3.28188i	0.785059	+	0.546981i
$37$	−3.89395	+	6.74451i	−0.640161	+	1.10879i	0.345236	+	0.938516i	$0.387799\pi$
$37$	−3.89395	+	6.74451i	−0.640161	+	1.10879i	−0.985397	+	0.170275i	$0.945534\pi$
$38$	−0.748891			−0.121486
$39$	−1.21596	+	3.87227i	−0.194709	+	0.620059i
$40$		−	3.51962i		−	0.556500i
$41$	−3.12737	−	5.41676i	−0.488413	−	0.845956i	0.511498	−	0.859284i	$-0.329091\pi$
$41$	−3.12737	−	5.41676i	−0.488413	−	0.845956i	−0.999911	+	0.0133282i	$0.995757\pi$
$42$	0.951677	+	0.952814i	0.146847	+	0.147022i
$43$	2.06191	−	3.57133i	0.314438	−	0.544623i	−0.664880	−	0.746950i	$-0.731517\pi$
$43$	2.06191	−	3.57133i	0.314438	−	0.544623i	0.979318	+	0.202328i	$0.0648506\pi$
$44$	6.45748	+	3.72823i	0.973501	+	0.562051i
$45$	0.778834	−	9.14772i	0.116102	−	1.36366i
$46$	0.437976	+	0.758597i	0.0645761	+	0.111849i
$47$	−2.02694	−	3.51076i	−0.295659	−	0.512097i	0.679479	−	0.733695i	$-0.262206\pi$
$47$	−2.02694	−	3.51076i	−0.295659	−	0.512097i	−0.975138	+	0.221598i	$0.928873\pi$
$48$	5.76605	+	1.81064i	0.832257	+	0.261343i
$49$	−3.99479	−	5.74818i	−0.570685	−	0.821169i
$50$	−1.11095	+	0.641408i	−0.157112	+	0.0907087i
$51$	−5.56106	−	1.74627i	−0.778704	−	0.244527i
$52$			4.48421i			0.621848i
$53$	−4.99439	+	2.88351i	−0.686033	+	0.396081i	−0.802124	−	0.597157i	$-0.796297\pi$
$53$	−4.99439	+	2.88351i	−0.686033	+	0.396081i	0.116091	+	0.993239i	$0.462963\pi$
$54$	−1.41279	−	0.579416i	−0.192256	−	0.0788486i
$55$		−	11.9243i		−	1.60787i
$56$	2.69658	+	1.40980i	0.360346	+	0.188392i
$57$	−4.30818	+	0.960372i	−0.570633	+	0.127204i
$58$	1.24616			0.163629
$59$	−2.34352	+	4.05910i	−0.305101	+	0.528450i	−0.977284	−	0.211935i	$-0.932023\pi$
$59$	−2.34352	+	4.05910i	−0.305101	+	0.528450i	0.672183	+	0.740385i	$0.265357\pi$
$60$	−2.20696	−	9.90033i	−0.284918	−	1.27813i
$61$	−1.38580	+	0.800092i	−0.177433	+	0.102441i	−0.586086	−	0.810249i	$-0.699332\pi$
$61$	−1.38580	+	0.800092i	−0.177433	+	0.102441i	0.408653	+	0.912690i	$0.365999\pi$
$62$	0.138922			0.0176432
$63$	6.69664	+	4.26088i	0.843697	+	0.536820i
$64$	6.00131			0.750164
$65$	6.21035	−	3.58555i	0.770299	−	0.444733i
$66$	−1.89219	−	0.594182i	−0.232913	−	0.0731388i
$67$	−0.787831	+	1.36456i	−0.0962489	+	0.166708i	−0.910129	−	0.414325i	$-0.864018\pi$
$67$	−0.787831	+	1.36456i	−0.0962489	+	0.166708i	0.813880	+	0.581033i	$0.197351\pi$
$68$	−6.43989			−0.780951
$69$	3.49238	+	3.80236i	0.420434	+	0.457750i
$70$	−0.0995964	−	2.37729i	−0.0119040	−	0.284141i
$71$		−	13.6132i		−	1.61559i	−0.589462	−	0.807796i	$-0.700660\pi$
$71$		−	13.6132i		−	1.61559i	0.589462	−	0.807796i	$-0.299340\pi$
$72$	−3.43786	−	0.292699i	−0.405156	−	0.0344948i
$73$	−0.856452	+	0.494473i	−0.100240	+	0.0578737i	−0.549282	−	0.835637i	$-0.685099\pi$
$73$	−0.856452	+	0.494473i	−0.100240	+	0.0578737i	0.449042	+	0.893511i	$0.351765\pi$
$74$		−	2.28862i		−	0.266047i
$75$	−5.56848	+	5.11453i	−0.642993	+	0.590575i
$76$	−4.22333	+	2.43834i	−0.484450	+	0.279697i
$77$	9.13588	+	4.77633i	1.04113	+	0.544313i
$78$	−0.259511	−	1.16415i	−0.0293838	−	0.131814i
$79$	4.63908	+	8.03512i	0.521937	+	0.904021i	0.999674	+	0.0255186i	$0.00812370\pi$
$79$	4.63908	+	8.03512i	0.521937	+	0.904021i	−0.477737	+	0.878503i	$0.658543\pi$
$80$	−5.33910	−	9.24760i	−0.596930	−	1.03391i
$81$	−8.87046	−	1.52149i	−0.985607	−	0.169054i
$82$	1.59182	+	0.919038i	0.175787	+	0.101491i
$83$	−5.49361	+	9.51520i	−0.603002	+	1.04443i	0.389362	+	0.921085i	$0.372695\pi$
$83$	−5.49361	+	9.51520i	−0.603002	+	1.04443i	−0.992364	+	0.123345i	$0.960638\pi$
$84$	8.46924	+	2.27475i	0.924069	+	0.248195i
$85$	5.14930	+	8.91884i	0.558519	+	0.967384i
$86$			1.21186i			0.130679i
$87$	7.16886	−	1.59807i	0.768582	−	0.171331i
$88$	−4.48133			−0.477712
$89$	2.15849	−	3.73861i	0.228799	−	0.396292i	−0.728653	−	0.684883i	$-0.759853\pi$
$89$	2.15849	−	3.73861i	0.228799	−	0.396292i	0.957452	+	0.288591i	$0.0931868\pi$
$90$	1.14591	+	2.44252i	0.120789	+	0.257464i
$91$	0.259511	+	6.19433i	0.0272041	+	0.649342i
$92$	4.93989	+	2.85205i	0.515019	+	0.297346i
$93$	0.799185	−	0.178153i	0.0828716	−	0.0184736i
$94$	1.03171	+	0.595655i	0.106412	+	0.0614371i
$95$	6.75390	+	3.89937i	0.692936	+	0.400067i
$96$	−5.62211	+	1.25327i	−0.573804	+	0.127911i
$97$	−4.98797	−	2.87980i	−0.506451	−	0.292400i	0.224923	−	0.974377i	$-0.427787\pi$
$97$	−4.98797	−	2.87980i	−0.506451	−	0.292400i	−0.731374	+	0.681977i	$0.761120\pi$
$98$	1.86128	+	0.875930i	0.188017	+	0.0884823i
$99$	−11.6473	−	0.991647i	−1.17060	−	0.0996642i
$100$	−4.17676	+	7.23437i	−0.417676	+	0.723437i
$101$	17.1580			1.70728			0.853642	−	0.520860i	$-0.174389\pi$
$101$	17.1580			1.70728			0.853642	+	0.520860i	$0.174389\pi$
$102$	1.67187	−	0.372690i	0.165540	−	0.0369018i
$103$			9.81983i			0.967577i	0.875185	+	0.483788i	$0.160740\pi$
$103$			9.81983i			0.967577i	−0.875185	+	0.483788i	$0.839260\pi$
$104$	−1.34751	−	2.33395i	−0.132134	−	0.228863i
$105$	−3.62157	−	13.5482i	−0.353429	−	1.32217i
$106$	0.847377	−	1.46770i	0.0823045	−	0.142556i
$107$	3.00501	+	1.73494i	0.290505	+	0.167723i	0.638170	−	0.769896i	$-0.279692\pi$
$107$	3.00501	+	1.73494i	0.290505	+	0.167723i	−0.347664	+	0.937619i	$0.613025\pi$
$108$	−9.85390	+	1.33237i	−0.948192	+	0.128207i
$109$	0.611066	+	1.05840i	0.0585295	+	0.101376i	0.893806	−	0.448455i	$-0.148025\pi$
$109$	0.611066	+	1.05840i	0.0585295	+	0.101376i	−0.835276	+	0.549831i	$0.814692\pi$
$110$	1.75209	+	3.03471i	0.167055	+	0.289348i
$111$	−2.93491	−	13.1659i	−0.278569	−	1.24965i
$112$	9.22374	−	0.386427i	0.871561	−	0.0365140i
$113$	−1.87681	+	1.08358i	−0.176555	+	0.101934i	−0.585673	−	0.810547i	$-0.699170\pi$
$113$	−1.87681	+	1.08358i	−0.176555	+	0.101934i	0.409118	+	0.912482i	$0.365836\pi$
$114$	0.955314	−	0.877435i	0.0894733	−	0.0821793i
$115$		−	9.12191i		−	0.850623i
$116$	7.02767	−	4.05743i	0.652503	−	0.376723i
$117$	−2.98580	−	6.36428i	−0.276037	−	0.588378i
$118$		−	1.37738i		−	0.126798i
$119$	−8.89582	+	0.372690i	−0.815479	+	0.0341644i
$120$	4.12374	+	4.48975i	0.376444	+	0.409856i
$121$	−4.18251			−0.380228
$122$	0.235123	−	0.407244i	0.0212870	−	0.0368702i
$123$	10.3359	+	3.24566i	0.931957	+	0.292651i
$124$	0.783445	−	0.452322i	0.0703555	−	0.0406198i
$125$	−1.94249			−0.173742
$126$	−2.33035	−	0.100418i	−0.207604	−	0.00894591i
$127$	2.74889			0.243925			0.121962	−	0.992535i	$-0.461081\pi$
$127$	2.74889			0.243925			0.121962	+	0.992535i	$0.461081\pi$
$128$	−7.28743	+	4.20740i	−0.644124	+	0.371885i
$129$	1.55408	+	6.97154i	0.136829	+	0.613810i
$130$	−1.05368	+	1.82503i	−0.0924141	+	0.160066i
$131$	−7.47821			−0.653375			−0.326687	−	0.945132i	$-0.605932\pi$
$131$	−7.47821			−0.653375			−0.326687	+	0.945132i	$0.605932\pi$
$132$	−12.6056	+	2.81000i	−1.09717	+	0.244580i
$133$	−5.69285	+	3.61265i	−0.493632	+	0.313256i
$134$		−	0.463039i		−	0.0400005i
$135$	9.72436	+	12.5817i	0.836940	+	1.08286i
$136$	3.35185	−	1.93519i	0.287418	−	0.165941i
$137$		−	12.2088i		−	1.04307i	−0.853231	−	0.521533i	$-0.825360\pi$
$137$		−	12.2088i		−	1.04307i	0.853231	−	0.521533i	$-0.174640\pi$
$138$	−1.44750	−	0.454542i	−0.123220	−	0.0386932i
$139$	11.5501	−	6.66842i	0.979663	−	0.565608i	0.0774943	−	0.996993i	$-0.475308\pi$
$139$	11.5501	−	6.66842i	0.979663	−	0.565608i	0.902168	+	0.431384i	$0.141975\pi$
$140$	−8.30198	−	13.0823i	−0.701645	−	1.10566i
$141$	6.69900	+	2.10360i	0.564157	+	0.177155i
$142$	2.00026	+	3.46454i	0.167858	+	0.290738i
$143$	−4.56528	−	7.90730i	−0.381768	−	0.661242i
$144$	−9.47681	+	4.44604i	−0.789734	+	0.370503i
$145$	−11.2386	−	6.48859i	−0.933312	−	0.538848i
$146$	0.145310	−	0.251685i	0.0120260	−	0.0208296i
$147$	11.8307	+	2.65212i	0.975783	+	0.218743i
$148$	−7.45161	−	12.9066i	−0.612519	−	1.06091i
$149$			8.47350i			0.694176i	0.937832	+	0.347088i	$0.112830\pi$
$149$			8.47350i			0.694176i	−0.937832	+	0.347088i	$0.887170\pi$
$150$	0.665668	−	2.11984i	0.0543515	−	0.173084i
$151$	−3.35654			−0.273152			−0.136576	−	0.990630i	$-0.543610\pi$
$151$	−3.35654			−0.273152			−0.136576	+	0.990630i	$0.543610\pi$
$152$	1.46545	−	2.53823i	0.118863	−	0.205877i
$153$	9.13990	−	4.28798i	0.738917	−	0.346662i
$154$	−3.02688	+	0.126811i	−0.243913	+	0.0102187i
$155$	−1.25288	−	0.723348i	−0.100633	−	0.0581007i
$156$	−5.25390	−	5.72023i	−0.420649	−	0.457985i
$157$	−14.4700	−	8.35426i	−1.15483	−	0.666743i	−0.204772	−	0.978810i	$-0.565645\pi$
$157$	−14.4700	−	8.35426i	−1.15483	−	0.666743i	−0.950060	+	0.312067i	$0.898979\pi$
$158$	−2.36128	−	1.36328i	−0.187853	−	0.108457i
$159$	2.99258	−	9.52997i	0.237327	−	0.755776i
$160$	8.81374	+	5.08862i	0.696787	+	0.402290i
$161$	6.98883	+	3.65383i	0.550797	+	0.287962i
$162$	2.48108	−	0.916163i	0.194932	−	0.0719806i
$163$	12.6662	−	21.9385i	0.992094	−	1.71836i	0.387363	−	0.921927i	$-0.373386\pi$
$163$	12.6662	−	21.9385i	0.992094	−	1.71836i	0.604731	−	0.796430i	$-0.293281\pi$
$164$	11.9693			0.934647
$165$	13.9710	+	15.2110i	1.08764	+	1.18418i
$166$		−	3.22881i		−	0.250604i
$167$	−0.875828	−	1.51698i	−0.0677736	−	0.117387i	0.830147	−	0.557544i	$-0.188256\pi$
$167$	−0.875828	−	1.51698i	−0.0677736	−	0.117387i	−0.897921	+	0.440157i	$0.854923\pi$
$168$	−5.09165	+	1.36104i	−0.392829	+	0.105007i
$169$	−3.75450	+	6.50298i	−0.288808	+	0.500229i
$170$	−2.62097	−	1.51322i	−0.201020	−	0.116059i
$171$	4.37046	−	6.27274i	0.334218	−	0.479689i
$172$	3.94575	+	6.83424i	0.300861	+	0.521106i
$173$	11.9633	+	20.7210i	0.909551	+	1.57539i	0.814689	+	0.579898i	$0.196908\pi$
$173$	11.9633	+	20.7210i	0.909551	+	1.57539i	0.0948622	+	0.995490i	$0.469759\pi$
$174$	−1.58965	+	1.46006i	−0.120511	+	0.110687i
$175$	−5.35096	+	10.2350i	−0.404495	+	0.773694i
$176$	−11.7745	+	6.79799i	−0.887533	+	0.512418i
$177$	−1.76634	−	7.92371i	−0.132766	−	0.595583i
$178$			1.26863i			0.0950875i
$179$	−21.9857	+	12.6935i	−1.64329	+	0.948755i	−0.663639	+	0.748053i	$0.730989\pi$
$179$	−21.9857	+	12.6935i	−1.64329	+	0.948755i	−0.979652	+	0.200702i	$0.935678\pi$
$180$	14.4150	+	10.0435i	1.07443	+	0.748595i
$181$			22.4032i			1.66522i	0.553859	+	0.832610i	$0.313155\pi$
$181$			22.4032i			1.66522i	−0.553859	+	0.832610i	$0.686845\pi$
$182$	−0.976207	−	1.53832i	−0.0723613	−	0.114028i
$183$	0.830354	−	2.64429i	0.0613815	−	0.195472i
$184$	−3.42816			−0.252728
$185$	−11.9165	+	20.6400i	−0.876121	+	1.51749i
$186$	−0.177214	+	0.162768i	−0.0129940	+	0.0119347i
$187$	11.3559	−	6.55631i	0.830423	−	0.479445i
$188$	7.75766			0.565786
$189$	−13.5347	+	2.41075i	−0.984505	+	0.175356i
$190$	−2.29181			−0.166265
$191$	−3.71434	+	2.14447i	−0.268760	+	0.155169i	−0.628324	−	0.777952i	$-0.716259\pi$
$191$	−3.71434	+	2.14447i	−0.268760	+	0.155169i	0.359564	+	0.933120i	$0.382925\pi$
$192$	−7.65550	+	7.03141i	−0.552488	+	0.507448i
$193$	11.6725	−	20.2173i	0.840203	−	1.45527i	−0.0495201	−	0.998773i	$-0.515769\pi$
$193$	11.6725	−	20.2173i	0.840203	−	1.45527i	0.889723	−	0.456501i	$-0.150897\pi$
$194$	1.69257			0.121520
$195$	−3.72117	+	11.8502i	−0.266478	+	0.848609i
$196$	13.3485	−	1.12044i	0.953467	−	0.0800313i
$197$			18.7811i			1.33809i	0.743220	+	0.669047i	$0.233298\pi$
$197$			18.7811i			1.33809i	−0.743220	+	0.669047i	$0.766702\pi$
$198$	3.10992	−	1.45902i	0.221013	−	0.103688i
$199$	−3.92927	+	2.26856i	−0.278539	+	0.160814i	−0.632762	−	0.774347i	$-0.718079\pi$
$199$	−3.92927	+	2.26856i	−0.278539	+	0.160814i	0.354223	+	0.935161i	$0.384745\pi$
$200$		−	5.02048i		−	0.355001i
$201$	−0.593797	−	2.66374i	−0.0418832	−	0.187886i
$202$	−4.36668	+	2.52111i	−0.307239	+	0.177384i
$203$	9.47295	−	6.01149i	0.664871	−	0.421924i
$204$	8.21496	−	7.54526i	0.575162	−	0.528274i
$205$	−9.57060	−	16.5768i	−0.668439	−	1.15777i
$206$	−1.44287	−	2.49913i	−0.100530	−	0.174123i
$207$	−8.91003	−	0.758597i	−0.619290	−	0.0527262i
$208$	−7.08101	−	4.08822i	−0.490980	−	0.283467i
$209$	4.96485	−	8.59937i	0.343426	−	0.594831i
$210$	2.91239	+	2.91587i	0.200974	+	0.201214i
$211$	−3.44148	−	5.96082i	−0.236921	−	0.410360i	0.722908	−	0.690944i	$-0.242805\pi$
$211$	−3.44148	−	5.96082i	−0.236921	−	0.410360i	−0.959829	+	0.280584i	$0.909472\pi$
$212$		−	11.0360i		−	0.757957i
$213$	15.9499	+	17.3655i	1.09287	+	1.18987i
$214$	−1.01969			−0.0697049
$215$	6.31000	−	10.9292i	0.430338	−	0.745368i
$216$	4.72840	−	3.65457i	0.321727	−	0.248662i
$217$	1.05605	−	0.670161i	0.0716890	−	0.0454935i
$218$	−0.311031	−	0.179574i	−0.0210657	−	0.0121623i
$219$	0.513175	−	1.63423i	0.0346772	−	0.110431i
$220$	19.7616	+	11.4094i	1.33233	+	0.769220i
$221$	6.82927	+	3.94288i	0.459387	+	0.265227i
$222$	2.68145	+	2.91945i	0.179967	+	0.195941i
$223$	−5.57176	−	3.21686i	−0.373113	−	0.215417i	0.301705	−	0.953401i	$-0.402444\pi$
$223$	−5.57176	−	3.21686i	−0.373113	−	0.215417i	−0.674818	+	0.737985i	$0.735778\pi$
$224$	−7.42908	+	4.71445i	−0.496376	+	0.314998i
$225$	1.11095	−	13.0486i	0.0740634	−	0.869904i
$226$	0.318430	−	0.551537i	0.0211816	−	0.0366877i
$227$	−19.7397			−1.31017			−0.655084	−	0.755556i	$-0.727367\pi$
$227$	−19.7397			−1.31017			−0.655084	+	0.755556i	$0.727367\pi$
$228$	2.53057	−	8.05869i	0.167591	−	0.533700i
$229$			10.9069i			0.720747i	0.932808	+	0.360373i	$0.117351\pi$
$229$			10.9069i			0.720747i	−0.932808	+	0.360373i	$0.882649\pi$
$230$	1.34033	+	2.32151i	0.0883785	+	0.153076i
$231$	−17.2502	+	4.61115i	−1.13498	+	0.303391i
$232$	−2.43852	+	4.22364i	−0.160097	+	0.277295i
$233$	−17.9944	−	10.3891i	−1.17885	−	0.680611i	−0.223104	−	0.974795i	$-0.571619\pi$
$233$	−17.9944	−	10.3891i	−1.17885	−	0.680611i	−0.955749	+	0.294184i	$0.904952\pi$
$234$	1.69501	+	1.18098i	0.110807	+	0.0772032i
$235$	−6.20298	−	10.7439i	−0.404638	−	0.700853i
$236$	−4.48466	−	7.76766i	−0.291927	−	0.505632i
$237$	−15.3321	−	4.81454i	−0.995925	−	0.312738i
$238$	2.20921	−	1.40195i	0.143202	−	0.0908752i
$239$	23.6739	−	13.6681i	1.53134	−	0.884119i	0.532039	−	0.846720i	$-0.321426\pi$
$239$	23.6739	−	13.6681i	1.53134	−	0.884119i	0.999300	−	0.0373991i	$-0.0119073\pi$
$240$	17.6457	+	5.54105i	1.13902	+	0.357673i
$241$			21.3259i			1.37372i	0.726788	+	0.686861i	$0.241012\pi$
$241$			21.3259i			1.37372i	−0.726788	+	0.686861i	$0.758988\pi$
$242$	1.06444	−	0.614556i	0.0684250	−	0.0395052i
$243$	13.0981	−	8.45216i	0.840245	−	0.542207i
$244$		−	3.06218i		−	0.196036i
$245$	−12.2251	−	17.5910i	−0.781036	−	1.12385i
$246$	−3.10737	+	0.692689i	−0.198119	+	0.0441643i
$247$	5.97159			0.379963
$248$	−0.271846	+	0.470851i	−0.0172622	+	0.0298991i
$249$	−4.14059	−	18.5745i	−0.262399	−	1.17711i
$250$	0.494361	−	0.285419i	0.0312661	−	0.0180515i
$251$	26.7381			1.68769			0.843847	−	0.536584i	$-0.180286\pi$
$251$	26.7381			1.68769			0.843847	+	0.536584i	$0.180286\pi$
$252$	−13.4689	+	7.02119i	−0.848459	+	0.442293i
$253$	−11.6144			−0.730193
$254$	−0.699589	+	0.403908i	−0.0438961	+	0.0253434i
$255$	−17.0183	−	5.34406i	−1.06573	−	0.334658i
$256$	−4.76489	+	8.25303i	−0.297805	+	0.515814i
$257$	−3.05279			−0.190428			−0.0952140	−	0.995457i	$-0.530354\pi$
$257$	−3.05279			−0.190428			−0.0952140	+	0.995457i	$0.530354\pi$
$258$	−1.41987	−	1.54590i	−0.0883975	−	0.0962434i
$259$	−11.0403	−	17.3974i	−0.686012	−	1.08102i
$260$			13.7229i			0.851058i
$261$	−7.27249	+	10.4379i	−0.450156	+	0.646090i
$262$	1.90319	−	1.09881i	0.117580	−	0.0678847i
$263$			16.2174i			1.00001i	0.866024	+	0.500003i	$0.166668\pi$
$263$			16.2174i			1.00001i	−0.866024	+	0.500003i	$0.833332\pi$
$264$	5.71655	−	5.25053i	0.351830	−	0.323148i
$265$	−15.2842	+	8.82433i	−0.938901	+	0.542074i
$266$	0.917996	−	1.75589i	0.0562860	−	0.107661i
$267$	1.62687	+	7.29808i	0.0995631	+	0.446635i
$268$	−1.50763	−	2.61128i	−0.0920929	−	0.159510i
$269$	−0.303255	−	0.525254i	−0.0184898	−	0.0320253i	0.856632	−	0.515927i	$-0.172552\pi$
$269$	−0.303255	−	0.525254i	−0.0184898	−	0.0320253i	−0.875122	+	0.483902i	$0.839219\pi$
$270$	−4.32352	−	1.77317i	−0.263121	−	0.107912i
$271$	19.8948	+	11.4863i	1.20852	+	0.697742i	0.962437	−	0.271505i	$-0.0875215\pi$
$271$	19.8948	+	11.4863i	1.20852	+	0.697742i	0.246088	+	0.969248i	$0.420855\pi$
$272$	5.87120	−	10.1692i	0.355994	−	0.616599i
$273$	−7.58859	−	7.59766i	−0.459282	−	0.459831i
$274$	1.79389	+	3.10711i	0.108373	+	0.187708i
$275$		−	17.0091i		−	1.02569i
$276$	−9.64309	+	2.14962i	−0.580446	+	0.129392i
$277$	13.2835			0.798125			0.399063	−	0.916924i	$-0.369336\pi$
$277$	13.2835			0.798125			0.399063	+	0.916924i	$0.369336\pi$
$278$	−1.95965	+	3.39421i	−0.117532	+	0.203571i
$279$	−0.810738	+	1.16362i	−0.0485376	+	0.0696640i
$280$	8.25228	+	4.31437i	0.493168	+	0.257833i
$281$	5.68377	+	3.28153i	0.339065	+	0.195759i	0.659859	−	0.751390i	$-0.270616\pi$
$281$	5.68377	+	3.28153i	0.339065	+	0.195759i	−0.320793	+	0.947149i	$0.603950\pi$
$282$	−2.01398	+	0.448952i	−0.119931	+	0.0267347i
$283$	2.57413	+	1.48617i	0.153016	+	0.0883437i	0.574553	−	0.818467i	$-0.305176\pi$
$283$	2.57413	+	1.48617i	0.153016	+	0.0883437i	−0.421537	+	0.906811i	$0.638509\pi$
$284$	22.5607	+	13.0254i	1.33873	+	0.772916i
$285$	−13.1842	+	2.93900i	−0.780965	+	0.174091i
$286$	2.32371	+	1.34160i	0.137404	+	0.0793303i
$287$	16.5340	−	0.692689i	0.975970	−	0.0408882i
$288$	5.70338	−	8.18583i	0.336075	−	0.482355i
$289$	2.83753	−	4.91475i	0.166914	−	0.289103i
$290$	3.81360			0.223942
$291$	9.73694	−	2.17054i	0.570789	−	0.127239i
$292$		−	1.89249i		−	0.110749i
$293$	−3.03087	−	5.24962i	−0.177065	−	0.306686i	0.763809	−	0.645443i	$-0.223327\pi$
$293$	−3.03087	−	5.24962i	−0.177065	−	0.306686i	−0.940874	+	0.338756i	$0.889994\pi$
$294$	−3.40059	+	1.06339i	−0.198327	+	0.0620179i
$295$	−7.17181	+	12.4219i	−0.417559	+	0.723234i
$296$	7.75686	+	4.47843i	0.450858	+	0.260303i
$297$	16.0196	−	12.3815i	0.929549	−	0.718447i
$298$	−1.24505	−	2.15649i	−0.0721239	−	0.124922i
$299$	−3.49238	−	6.04899i	−0.201970	−	0.349822i
$300$	−3.14807	−	14.1221i	−0.181754	−	0.815340i
$301$	5.84603	+	9.21222i	0.336959	+	0.530984i
$302$	0.854235	−	0.493193i	0.0491557	−	0.0283801i
$303$	−21.8874	+	20.1031i	−1.25740	+	1.15489i
$304$		−	8.89207i		−	0.509995i
$305$	−4.24092	+	2.44850i	−0.242834	+	0.140201i
$306$	−1.69604	+	2.43425i	−0.0969560	+	0.139157i
$307$			21.6030i			1.23295i	0.787375	+	0.616474i	$0.211439\pi$
$307$			21.6030i			1.23295i	−0.787375	+	0.616474i	$0.788561\pi$
$308$	−16.6570	+	10.5705i	−0.949122	+	0.602308i
$309$	−11.5054	−	12.5265i	−0.654517	−	0.712610i
$310$	0.425140			0.0241463
$311$	5.51171	−	9.54656i	0.312540	−	0.541336i	−0.666371	−	0.745620i	$-0.732153\pi$
$311$	5.51171	−	9.54656i	0.312540	−	0.541336i	0.978912	+	0.204284i	$0.0654868\pi$
$312$	4.45349	+	1.39847i	0.252129	+	0.0791730i
$313$	−11.7383	+	6.77710i	−0.663487	+	0.383064i	−0.793604	−	0.608434i	$-0.791798\pi$
$313$	−11.7383	+	6.77710i	−0.663487	+	0.383064i	0.130117	+	0.991499i	$0.458465\pi$
$314$	4.91012			0.277094
$315$	20.4935	+	13.0394i	1.15468	+	0.734689i
$316$	−17.7551			−0.998800
$317$	−9.65977	+	5.57707i	−0.542547	+	0.313240i	−0.746111	−	0.665822i	$-0.768081\pi$
$317$	−9.65977	+	5.57707i	−0.542547	+	0.313240i	0.203564	+	0.979062i	$0.434748\pi$
$318$	0.638677	+	2.86508i	0.0358152	+	0.160665i
$319$	−8.26156	+	14.3094i	−0.462559	+	0.801175i
$320$	18.3656			1.02667
$321$	−5.86604	+	1.30765i	−0.327411	+	0.0729857i
$322$	−2.31552	+	0.0970085i	−0.129039	+	0.00540607i
$323$			8.57595i			0.477179i
$324$	11.0089	−	13.2449i	0.611608	−	0.735827i
$325$	8.85862	−	5.11453i	0.491388	−	0.283703i
$326$			7.44442i			0.412308i
$327$	−2.01956	−	0.634178i	−0.111682	−	0.0350701i
$328$	−6.22982	+	3.59679i	−0.343984	+	0.198599i
$329$	10.7161	−	0.448952i	0.590800	−	0.0247515i
$330$	−5.79063	−	1.81836i	−0.318763	−	0.100097i
$331$	9.51009	+	16.4720i	0.522722	+	0.905380i	0.999650	+	0.0264385i	$0.00841661\pi$
$331$	9.51009	+	16.4720i	0.522722	+	0.905380i	−0.476929	+	0.878942i	$0.658250\pi$
$332$	−10.5128	−	18.2087i	−0.576964	−	0.999331i
$333$	19.1696	+	13.3562i	1.05049	+	0.731915i
$334$	0.445794	+	0.257379i	0.0243927	+	0.0140832i
$335$	−2.41098	+	4.17593i	−0.131726	+	0.228156i
$336$	−11.3134	+	11.2999i	−0.617195	+	0.616459i
$337$	3.32635	+	5.76140i	0.181198	+	0.313843i	0.942289	−	0.334802i	$-0.108669\pi$
$337$	3.32635	+	5.76140i	0.181198	+	0.313843i	−0.761091	+	0.648645i	$0.775336\pi$
$338$		−	2.20666i		−	0.120027i
$339$	1.12456	−	3.58120i	0.0610777	−	0.194504i
$340$	−19.7078			−1.06881
$341$	−0.921000	+	1.59522i	−0.0498749	+	0.0863859i
$342$	−0.190592	+	2.23858i	−0.0103060	+	0.121048i
$343$	18.3743	−	2.32024i	0.992121	−	0.125281i
$344$	−4.10738	−	2.37140i	−0.221455	−	0.127857i
$345$	10.6876	+	11.6362i	0.575403	+	0.626475i
$346$	−6.08927	−	3.51564i	−0.327361	−	0.189002i
$347$	−23.0796	−	13.3250i	−1.23898	−	0.715325i	−0.270094	−	0.962834i	$-0.587055\pi$
$347$	−23.0796	−	13.3250i	−1.23898	−	0.715325i	−0.968886	+	0.247509i	$0.920388\pi$
$348$	−4.21089	+	13.4097i	−0.225728	+	0.718837i
$349$	20.5135	+	11.8435i	1.09806	+	0.633966i	0.935711	−	0.352768i	$-0.114759\pi$
$349$	20.5135	+	11.8435i	1.09806	+	0.633966i	0.162350	+	0.986733i	$0.448093\pi$
$350$	−0.142067	−	3.39104i	−0.00759380	−	0.181258i
$351$	11.2655	+	4.62022i	0.601306	+	0.246609i
$352$	6.47905	−	11.2221i	0.345335	−	0.598137i
$353$	4.58845			0.244218			0.122109	−	0.992517i	$-0.461034\pi$
$353$	4.58845			0.244218			0.122109	+	0.992517i	$0.461034\pi$
$354$	1.61380	+	1.75704i	0.0857725	+	0.0933854i
$355$		−	41.6602i		−	2.21109i
$356$	4.13057	+	7.15435i	0.218920	+	0.379180i
$357$	10.9112	−	10.8982i	0.577481	−	0.576792i
$358$	3.73022	−	6.46094i	0.197148	−	0.341471i
$359$	5.30942	+	3.06540i	0.280221	+	0.161785i	0.633523	−	0.773724i	$-0.281608\pi$
$359$	5.30942	+	3.06540i	0.280221	+	0.161785i	−0.353303	+	0.935509i	$0.614941\pi$
$360$	−10.5208	−	0.895737i	−0.554494	−	0.0472095i
$361$	−6.25288	−	10.8303i	−0.329099	−	0.570016i
$362$	−3.29182	−	5.70159i	−0.173014	−	0.299669i
$363$	5.33537	−	4.90042i	0.280034	−	0.257205i
$364$	−10.5139	−	5.49678i	−0.551079	−	0.288110i
$365$	−2.62097	+	1.51322i	−0.137188	+	0.0792056i
$366$	0.177214	+	0.794976i	0.00926315	+	0.0415541i
$367$		−	26.4264i		−	1.37945i	−0.724072	−	0.689725i	$-0.757732\pi$
$367$		−	26.4264i		−	1.37945i	0.724072	−	0.689725i	$-0.242268\pi$
$368$	−9.00732	+	5.20038i	−0.469539	+	0.271088i
$369$	−16.9876	+	7.96973i	−0.884340	+	0.414888i
$370$		−	7.00381i		−	0.364111i
$371$	−0.638677	−	15.2448i	−0.0331585	−	0.791468i
$372$	−0.469431	+	1.49492i	−0.0243388	+	0.0775079i
$373$	20.1162			1.04158			0.520789	−	0.853686i	$-0.325638\pi$
$373$	20.1162			1.04158			0.520789	+	0.853686i	$0.325638\pi$
$374$	−1.92670	+	3.33714i	−0.0996273	+	0.172560i
$375$	2.47791	−	2.27591i	0.127959	−	0.117527i
$376$	−4.03772	+	2.33118i	−0.208230	+	0.120221i
$377$	−9.93679			−0.511771
$378$	3.09034	−	2.60225i	0.158950	−	0.133845i
$379$	−17.4561			−0.896660			−0.448330	−	0.893868i	$-0.647981\pi$
$379$	−17.4561			−0.896660			−0.448330	+	0.893868i	$0.647981\pi$
$380$	−12.9245	+	7.46199i	−0.663015	+	0.382792i
$381$	−3.50659	+	3.22072i	−0.179648	+	0.165003i
$382$	0.630195	−	1.09153i	0.0322436	−	0.0558476i
$383$	−28.0633			−1.43397			−0.716985	−	0.697089i	$-0.754478\pi$
$383$	−28.0633			−1.43397			−0.716985	+	0.697089i	$0.754478\pi$
$384$	4.36654	−	13.9054i	0.222829	−	0.709607i
$385$	27.9583	+	14.6168i	1.42488	+	0.744944i
$386$			6.86037i			0.349183i
$387$	−10.1506	−	7.07232i	−0.515985	−	0.359506i
$388$	9.54517	−	5.51091i	0.484583	−	0.279774i
$389$		−	34.2392i		−	1.73600i	−0.496566	−	0.867999i	$-0.665406\pi$
$389$		−	34.2392i		−	1.73600i	0.496566	−	0.867999i	$-0.334594\pi$
$390$	−0.794173	−	3.56262i	−0.0402145	−	0.180400i
$391$	8.68710	−	5.01550i	0.439325	−	0.253645i
$392$	−6.61098	+	4.59441i	−0.333905	+	0.232053i
$393$	9.53949	−	8.76181i	0.481203	−	0.441975i
$394$	−2.75959	−	4.77975i	−0.139026	−	0.240800i
$395$	14.1968	+	24.5896i	0.714320	+	1.23724i
$396$	12.7878	−	18.3538i	0.642610	−	0.922312i
$397$	−11.2926	−	6.51981i	−0.566762	−	0.327220i	0.189093	−	0.981959i	$-0.439445\pi$
$397$	−11.2926	−	6.51981i	−0.566762	−	0.327220i	−0.755855	+	0.654739i	$0.772778\pi$
$398$	0.666662	−	1.15469i	0.0334167	−	0.0578795i
$399$	3.02926	−	11.2784i	0.151653	−	0.564627i
$400$	−7.61585	−	13.1910i	−0.380792	−	0.659552i
$401$			18.3532i			0.916514i	0.888820	+	0.458257i	$0.151526\pi$
$401$			18.3532i			0.916514i	−0.888820	+	0.458257i	$0.848474\pi$
$402$	0.542517	+	0.590669i	0.0270583	+	0.0294599i
$403$	−1.10775			−0.0551812
$404$	−16.4171	+	28.4353i	−0.816782	+	1.41471i
$405$	−27.1460	−	4.65616i	−1.34890	−	0.231366i
$406$	−1.52756	+	2.92182i	−0.0758113	+	0.145007i
$407$	26.2798	+	15.1727i	1.30264	+	0.752081i
$408$	−2.00838	+	6.39577i	−0.0994298	+	0.316638i
$409$	−5.60133	−	3.23393i	−0.276968	−	0.159907i	0.355082	−	0.934835i	$-0.384453\pi$
$409$	−5.60133	−	3.23393i	−0.276968	−	0.159907i	−0.632050	+	0.774928i	$0.717786\pi$
$410$	4.87140	+	2.81251i	0.240581	+	0.138900i
$411$	14.3043	+	15.5740i	0.705581	+	0.768207i
$412$	−16.2740	−	9.39581i	−0.801764	−	0.462899i
$413$	−6.64448	−	10.4704i	−0.326953	−	0.515216i
$414$	2.37905	−	1.11613i	0.116924	−	0.0548548i
$415$	−16.8119	+	29.1191i	−0.825265	+	1.42940i
$416$	7.79284			0.382075
$417$	−6.92065	+	22.0390i	−0.338906	+	1.07926i
$418$			2.91804i			0.142726i
$419$	−7.11542	−	12.3243i	−0.347611	−	0.602080i	0.638214	−	0.769859i	$-0.279674\pi$
$419$	−7.11542	−	12.3243i	−0.347611	−	0.602080i	−0.985825	+	0.167779i	$0.946340\pi$
$420$	25.9182	+	6.96134i	1.26468	+	0.339678i
$421$	15.1718	−	26.2784i	0.739429	−	1.28073i	−0.213324	−	0.976982i	$-0.568429\pi$
$421$	15.1718	−	26.2784i	0.739429	−	1.28073i	0.952753	−	0.303747i	$-0.0982378\pi$
$422$	1.75170	+	1.01135i	0.0852716	+	0.0492316i
$423$	−11.0102	+	5.16541i	−0.535333	+	0.251151i
$424$	3.31633	+	5.74405i	0.161055	+	0.278956i
$425$	7.34510	+	12.7221i	0.356290	+	0.617112i
$426$	−6.61081	−	2.07591i	−0.320295	−	0.100578i
$427$	−0.177214	−	4.22998i	−0.00857601	−	0.204703i
$428$	−5.75051	+	3.32006i	−0.277962	+	0.160481i
$429$	15.0882	+	4.73796i	0.728465	+	0.228751i
$430$			3.70863i			0.178846i
$431$	2.12663	−	1.22781i	0.102436	−	0.0591415i	−0.447907	−	0.894080i	$-0.647830\pi$
$431$	2.12663	−	1.22781i	0.102436	−	0.0591415i	0.550343	+	0.834939i	$0.314497\pi$
$432$	6.87979	−	16.7750i	0.331004	−	0.807086i
$433$		−	12.4545i		−	0.598525i	−0.954171	−	0.299262i	$-0.903259\pi$
$433$		−	12.4545i		−	0.598525i	0.954171	−	0.299262i	$-0.0967406\pi$
$434$	−0.170292	+	0.325725i	−0.00817428	+	0.0156353i
$435$	21.9386	−	4.89052i	1.05188	−	0.234483i
$436$	−2.33872			−0.112004
$437$	3.79805	−	6.57841i	0.181685	−	0.314688i
$438$	0.109522	+	0.491311i	0.00523317	+	0.0234757i
$439$	−15.1815	+	8.76502i	−0.724571	+	0.418331i	−0.816433	−	0.577440i	$-0.804052\pi$
$439$	−15.1815	+	8.76502i	−0.724571	+	0.418331i	0.0918615	+	0.995772i	$0.470718\pi$
$440$	−13.7141			−0.653794
$441$	−18.1991	+	10.4783i	−0.866622	+	0.498966i
$442$	−2.31739			−0.110227
$443$	7.79825	−	4.50232i	0.370506	−	0.213912i	−0.303173	−	0.952935i	$-0.598046\pi$
$443$	7.79825	−	4.50232i	0.370506	−	0.213912i	0.673680	+	0.739024i	$0.264713\pi$
$444$	24.6275	+	7.73346i	1.16877	+	0.367014i
$445$	6.60555	−	11.4411i	0.313133	−	0.542362i
$446$	1.89067			0.0895260
$447$	−9.92793	−	10.8091i	−0.469575	−	0.511254i
$448$	−7.35645	+	14.0710i	−0.347560	+	0.664792i
$449$		−	30.8120i		−	1.45411i	−0.686581	−	0.727054i	$-0.740889\pi$
$449$		−	30.8120i		−	1.45411i	0.686581	−	0.727054i	$-0.259111\pi$
$450$	1.63455	+	3.48407i	0.0770535	+	0.164241i
$451$	−21.1063	+	12.1857i	−0.993856	+	0.573803i
$452$		−	4.14715i		−	0.195065i
$453$	4.28173	−	3.93268i	0.201173	−	0.184773i
$454$	5.02371	−	2.90044i	0.235775	−	0.136125i
$455$	0.794173	+	18.9563i	0.0372314	+	0.888686i
$456$	1.10452	+	4.95484i	0.0517240	+	0.232032i
$457$	−6.91430	−	11.9759i	−0.323437	−	0.560210i	0.657758	−	0.753230i	$-0.271505\pi$
$457$	−6.91430	−	11.9759i	−0.323437	−	0.560210i	−0.981195	+	0.193020i	$0.938172\pi$
$458$	−1.60260	−	2.77578i	−0.0748846	−	0.129704i
$459$	−6.63521	+	16.1786i	−0.309705	+	0.755153i
$460$	15.1174	+	8.72803i	0.704852	+	0.406947i
$461$	−6.16989	+	10.6866i	−0.287360	+	0.497723i	−0.973179	−	0.230050i	$-0.926111\pi$
$461$	−6.16989	+	10.6866i	−0.287360	+	0.497723i	0.685818	+	0.727773i	$0.259444\pi$
$462$	3.71262	−	3.70819i	0.172727	−	0.172520i
$463$	6.37802	+	11.0471i	0.296412	+	0.513401i	0.975312	−	0.220830i	$-0.0708765\pi$
$463$	6.37802	+	11.0471i	0.296412	+	0.513401i	−0.678900	+	0.734230i	$0.737543\pi$
$464$			14.7965i			0.686910i
$465$	2.44572	−	0.545196i	0.113418	−	0.0252828i
$466$	6.10606			0.282858
$467$	5.48999	−	9.50894i	0.254046	−	0.440021i	−0.710590	−	0.703607i	$-0.751572\pi$
$467$	5.48999	−	9.50894i	0.254046	−	0.440021i	0.964636	+	0.263585i	$0.0849051\pi$
$468$	13.4041	+	1.14123i	0.619607	+	0.0527532i
$469$	−2.23370	−	3.51988i	−0.103143	−	0.162533i
$470$	3.15730	+	1.82287i	0.145635	+	0.0840825i
$471$	28.2467	−	6.29670i	1.30154	−	0.290137i
$472$	4.66837	+	2.69528i	0.214879	+	0.124061i
$473$	−13.9156	−	8.03417i	−0.639840	−	0.369412i
$474$	4.60941	−	1.02752i	0.211717	−	0.0471956i
$475$	9.63396	+	5.56217i	0.442036	+	0.255210i
$476$	7.89406	−	15.0993i	0.361824	−	0.692075i
$477$	7.34829	+	15.6630i	0.336455	+	0.717160i
$478$	−4.01665	+	6.95704i	−0.183717	+	0.318208i
$479$	−11.1946			−0.511493			−0.255747	−	0.966744i	$-0.582321\pi$
$479$	−11.1946			−0.511493			−0.255747	+	0.966744i	$0.582321\pi$
$480$	−17.2052	+	3.83535i	−0.785305	+	0.175059i
$481$			18.2493i			0.832096i
$482$	−3.13352	−	5.42741i	−0.142728	−	0.247212i
$483$	−13.1962	+	3.52747i	−0.600448	+	0.160505i
$484$	4.00191	−	6.93152i	0.181905	−	0.315069i
$485$	−15.2645	−	8.81298i	−0.693126	−	0.400177i
$486$	−2.09154	+	4.07563i	−0.0948740	+	0.184874i
$487$	−1.48332	−	2.56919i	−0.0672158	−	0.116421i	0.830459	−	0.557080i	$-0.188078\pi$
$487$	−1.48332	−	2.56919i	−0.0672158	−	0.116421i	−0.897675	+	0.440659i	$0.854745\pi$
$488$	0.920185	+	1.59381i	0.0416548	+	0.0721483i
$489$	9.54666	+	42.8259i	0.431715	+	1.93665i
$490$	5.69601	+	2.68058i	0.257319	+	0.121096i
$491$	−20.1795	+	11.6507i	−0.910690	+	0.525787i	−0.880653	−	0.473762i	$-0.842896\pi$
$491$	−20.1795	+	11.6507i	−0.910690	+	0.525787i	−0.0300367	+	0.999549i	$0.509562\pi$
$492$	−15.2685	+	14.0238i	−0.688358	+	0.632241i
$493$		−	14.2705i		−	0.642710i
$494$	−1.51976	+	0.877435i	−0.0683773	+	0.0394776i
$495$	−35.6438	−	3.03471i	−1.60207	−	0.136400i
$496$			1.64952i			0.0740654i
$497$	31.9183	+	16.6872i	1.43173	+	0.748523i
$498$	3.78301	+	4.11878i	0.169521	+	0.184567i
$499$	−4.58592			−0.205294			−0.102647	−	0.994718i	$-0.532731\pi$
$499$	−4.58592			−0.205294			−0.102647	+	0.994718i	$0.532731\pi$
$500$	1.85862	−	3.21922i	0.0831198	−	0.143968i
$501$	2.89460	+	0.908955i	0.129321	+	0.0406091i
$502$	−6.80480	+	3.92875i	−0.303713	+	0.175349i
$503$	23.1383			1.03169			0.515844	−	0.856683i	$-0.327479\pi$
$503$	23.1383			1.03169			0.515844	+	0.856683i	$0.327479\pi$
$504$	4.90043	−	7.70180i	0.218283	−	0.343065i
$505$	52.5081			2.33658
$506$	2.95585	−	1.70656i	0.131404	−	0.0758660i
$507$	−2.82981	−	12.6944i	−0.125676	−	0.563777i
$508$	−2.63020	+	4.55563i	−0.116696	+	0.202123i
$509$	9.65706			0.428042			0.214021	−	0.976829i	$-0.431344\pi$
$509$	9.65706			0.428042			0.214021	+	0.976829i	$0.431344\pi$
$510$	5.11637	−	1.14053i	0.226557	−	0.0505036i
$511$	−0.109522	−	2.61421i	−0.00484497	−	0.115646i
$512$		−	19.6301i		−	0.867536i
$513$	1.77430	+	13.1224i	0.0783374	+	0.579367i
$514$	0.776931	−	0.448561i	0.0342690	−	0.0197852i
$515$			30.0513i			1.32422i
$516$	−13.0406	−	4.09499i	−0.574083	−	0.180272i
$517$	−13.6796	+	7.89791i	−0.601627	+	0.347350i
$518$	5.36603	+	2.80541i	0.235770	+	0.123263i
$519$	−39.5384	−	12.4158i	−1.73555	−	0.544992i
$520$	−4.12374	−	7.14252i	−0.180838	−	0.313220i
$521$	−5.00035	−	8.66086i	−0.219069	−	0.379439i	0.735454	−	0.677574i	$-0.236969\pi$
$521$	−5.00035	−	8.66086i	−0.219069	−	0.379439i	−0.954524	+	0.298135i	$0.903635\pi$
$522$	0.317147	−	3.72501i	0.0138811	−	0.163039i
$523$	−10.7796	−	6.22361i	−0.471359	−	0.272139i	0.245449	−	0.969409i	$-0.421065\pi$
$523$	−10.7796	−	6.22361i	−0.471359	−	0.272139i	−0.716809	+	0.697270i	$0.754398\pi$
$524$	7.15531	−	12.3934i	0.312581	−	0.541406i
$525$	−5.16591	−	19.3256i	−0.225459	−	0.843437i
$526$	−2.38289	−	4.12729i	−0.103899	−	0.179959i
$527$		−	1.59087i		−	0.0692995i
$528$	7.05511	−	22.4672i	0.307034	−	0.977761i
$529$	14.1151			0.613700
$530$	2.59320	−	4.49156i	0.112641	−	0.195101i
$531$	11.5370	+	8.03826i	0.500662	+	0.348831i
$532$	−0.540075	−	12.8912i	−0.0234152	−	0.558904i
$533$	−12.6930	−	7.32833i	−0.549797	−	0.317425i
$534$	−1.48638	−	1.61831i	−0.0643219	−	0.0700310i
$535$	9.19615	+	5.30940i	0.397584	+	0.229545i
$536$	1.56938	+	0.906084i	0.0677870	+	0.0391369i
$537$	13.1736	−	41.9517i	0.568482	−	1.81035i
$538$	0.154356	+	0.0891175i	0.00665476	+	0.00384213i
$539$	−22.3977	+	15.5656i	−0.964735	+	0.670458i
$540$	−30.1556	+	4.07740i	−1.29769	+	0.175463i
$541$	6.96514	−	12.0640i	0.299455	−	0.518671i	−0.676557	−	0.736391i	$-0.736529\pi$
$541$	6.96514	−	12.0640i	0.299455	−	0.518671i	0.976011	+	0.217720i	$0.0698619\pi$
$542$	−6.75094			−0.289978
$543$	−26.2486	−	28.5784i	−1.12644	−	1.22642i
$544$			11.1915i			0.479831i
$545$	1.87003	+	3.23898i	0.0801032	+	0.138743i
$546$	3.04764	+	0.818564i	0.130427	+	0.0350313i
$547$	−21.6768	+	37.5454i	−0.926834	+	1.60532i	−0.138250	+	0.990397i	$0.544148\pi$
$547$	−21.6768	+	37.5454i	−0.926834	+	1.60532i	−0.788584	+	0.614926i	$0.789186\pi$
$548$	20.2331	+	11.6816i	0.864316	+	0.499013i
$549$	2.03894	+	4.34604i	0.0870198	+	0.185484i
$550$	2.49923	+	4.32879i	0.106567	+	0.184580i
$551$	−5.40325	−	9.35870i	−0.230186	−	0.398694i
$552$	4.37309	−	4.01659i	0.186131	−	0.170957i
$553$	−24.5262	+	1.02752i	−1.04296	+	0.0436947i
$554$	−3.38062	+	1.95180i	−0.143629	+	0.0829241i
$555$	−8.98162	−	40.2911i	−0.381248	−	1.71026i
$556$			25.5219i			1.08237i
$557$	31.1339	−	17.9752i	1.31919	−	0.761632i	0.335588	−	0.942009i	$-0.391065\pi$
$557$	31.1339	−	17.9752i	1.31919	−	0.761632i	0.983598	+	0.180377i	$0.0577317\pi$
$558$	0.0353555	−	0.415265i	0.00149672	−	0.0175796i
$559$		−	9.66329i		−	0.408714i
$560$	28.2271	−	1.18257i	1.19281	−	0.0499728i
$561$	−6.80430	+	21.6685i	−0.287278	+	0.914846i
$562$	−1.92868			−0.0813565
$563$	3.05554	−	5.29235i	0.128776	−	0.223046i	−0.794427	−	0.607360i	$-0.792229\pi$
$563$	3.05554	−	5.29235i	0.128776	−	0.223046i	0.923202	+	0.384314i	$0.125562\pi$
$564$	−9.89596	+	9.08922i	−0.416695	+	0.382725i
$565$	−5.74354	+	3.31603i	−0.241633	+	0.139507i
$566$	−0.873481			−0.0367151
$567$	14.4408	−	18.9331i	0.606458	−	0.795116i
$568$	−15.6566			−0.656935
$569$	16.7182	−	9.65223i	0.700861	−	0.404642i	−0.106807	−	0.994280i	$-0.534063\pi$
$569$	16.7182	−	9.65223i	0.700861	−	0.404642i	0.807668	+	0.589637i	$0.200729\pi$
$570$	2.92352	−	2.68519i	0.122453	−	0.112470i
$571$	−6.36118	+	11.0179i	−0.266207	+	0.461085i	−0.967879	−	0.251416i	$-0.919104\pi$
$571$	−6.36118	+	11.0179i	−0.266207	+	0.461085i	0.701672	+	0.712500i	$0.252437\pi$
$572$	17.4726			0.730567
$573$	2.22558	−	7.08745i	0.0929751	−	0.296083i
$574$	−4.10609	+	2.60570i	−0.171385	+	0.108760i
$575$		−	13.0118i		−	0.542628i
$576$	1.52732	−	17.9390i	0.0636385	−	0.747460i
$577$	7.05520	−	4.07332i	0.293712	−	0.169575i	−0.345903	−	0.938270i	$-0.612427\pi$
$577$	7.05520	−	4.07332i	0.293712	−	0.169575i	0.639615	+	0.768696i	$0.279094\pi$
$578$			1.66773i			0.0693683i
$579$	8.79767	+	39.4659i	0.365619	+	1.64015i
$580$	21.5066	−	12.4168i	0.893012	−	0.515581i
$581$	−15.5757	−	24.5444i	−0.646191	−	1.01827i
$582$	−2.15911	+	1.98309i	−0.0894979	+	0.0822019i
$583$	11.2355	+	19.4605i	0.465328	+	0.805973i
$584$	0.568693	+	0.985005i	0.0235327	+	0.0407598i
$585$	−9.13735	−	19.4764i	−0.377783	−	0.805251i
$586$	1.54270	+	0.890680i	0.0637285	+	0.0367937i
$587$	−12.3041	+	21.3113i	−0.507843	+	0.879610i	0.492116	+	0.870530i	$0.336224\pi$
$587$	−12.3041	+	21.3113i	−0.507843	+	0.879610i	−0.999959	+	0.00908019i	$0.997110\pi$
$588$	−15.7151	+	17.0690i	−0.648081	+	0.703915i
$589$	−0.602354	−	1.04331i	−0.0248196	−	0.0429888i
$590$		−	4.21515i		−	0.173535i
$591$	−22.0047	−	23.9578i	−0.905153	−	0.985492i
$592$	27.1743			1.11686
$593$	18.9321	−	32.7913i	0.777447	−	1.34658i	−0.155962	−	0.987763i	$-0.549848\pi$
$593$	18.9321	−	32.7913i	0.777447	−	1.34658i	0.933409	−	0.358814i	$-0.116819\pi$
$594$	−2.25768	+	5.50490i	−0.0926338	+	0.225869i
$595$	−27.2236	+	1.14053i	−1.11606	+	0.0467572i
$596$	−14.0428	−	8.10762i	−0.575216	−	0.332101i
$597$	2.35437	−	7.49757i	0.0963579	−	0.306855i
$598$	1.77761	+	1.02631i	0.0726920	+	0.0419687i
$599$	9.22572	+	5.32647i	0.376953	+	0.217634i	0.676492	−	0.736450i	$-0.263499\pi$
$599$	9.22572	+	5.32647i	0.376953	+	0.217634i	−0.299539	+	0.954084i	$0.596833\pi$
$600$	5.88221	+	6.40431i	0.240140	+	0.261455i
$601$	−39.8636	−	23.0153i	−1.62607	−	0.938812i	−0.985250	−	0.171122i	$-0.945261\pi$
$601$	−39.8636	−	23.0153i	−1.62607	−	0.938812i	−0.640821	−	0.767691i	$-0.721406\pi$
$602$	−2.84140	−	1.48551i	−0.115807	−	0.0605449i
$603$	3.87843	+	2.70225i	0.157942	+	0.110044i
$604$	3.21161	−	5.56267i	0.130679	−	0.226342i
$605$	−12.7996			−0.520378
$606$	2.61646	−	8.33222i	0.106287	−	0.338473i
$607$			4.31931i			0.175315i	0.996151	+	0.0876576i	$0.0279381\pi$
$607$			4.31931i			0.175315i	−0.996151	+	0.0876576i	$0.972062\pi$
$608$	4.23745	+	7.33947i	0.171851	+	0.297655i
$609$	−5.04072	+	18.7674i	−0.204260	+	0.760494i
$610$	0.719539	−	1.24628i	0.0291333	−	0.0504603i
$611$	−8.22672	−	4.74970i	−0.332818	−	0.192152i
$612$	−1.63894	+	19.2500i	−0.0662503	+	0.778136i
$613$	14.3838	+	24.9135i	0.580956	+	1.00624i	0.995366	+	0.0961549i	$0.0306544\pi$
$613$	14.3838	+	24.9135i	0.580956	+	1.00624i	−0.414411	+	0.910090i	$0.636012\pi$
$614$	−3.17423	−	5.49793i	−0.128102	−	0.221878i
$615$	31.6307	+	9.93259i	1.27547	+	0.400521i
$616$	5.49325	−	10.5072i	0.221329	−	0.423346i
$617$	0.935498	−	0.540110i	0.0376617	−	0.0217440i	−0.481051	−	0.876693i	$-0.659745\pi$
$617$	0.935498	−	0.540110i	0.0376617	−	0.0217440i	0.518713	+	0.854949i	$0.326411\pi$
$618$	4.76868	+	1.49745i	0.191824	+	0.0602362i
$619$			7.58787i			0.304982i	0.988305	+	0.152491i	$0.0487295\pi$
$619$			7.58787i			0.304982i	−0.988305	+	0.152491i	$0.951270\pi$
$620$	2.39755	−	1.38423i	0.0962881	−	0.0555920i
$621$	12.2548	−	9.47169i	0.491767	−	0.380086i
$622$			3.23944i			0.129890i
$623$	6.11985	+	9.64371i	0.245187	+	0.386367i
$624$	13.8227	−	3.08134i	0.553352	−	0.123352i
$625$	−27.7708			−1.11083
$626$	1.99158	−	3.44952i	0.0795996	−	0.137871i
$627$	3.74206	+	16.7867i	0.149444	+	0.670397i
$628$	27.6904	−	15.9871i	1.10497	−	0.637953i
$629$	−26.2082			−1.04499
$630$	−7.13151	−	0.307305i	−0.284126	−	0.0122433i
$631$	35.0387			1.39487			0.697435	−	0.716648i	$-0.254325\pi$
$631$	35.0387			1.39487			0.697435	+	0.716648i	$0.254325\pi$
$632$	9.24118	−	5.33540i	0.367595	−	0.212231i
$633$	11.3740	+	3.57165i	0.452078	+	0.141960i
$634$	1.63893	−	2.83871i	0.0650903	−	0.112740i
$635$	8.41235			0.333834
$636$	12.9303	+	14.0780i	0.512719	+	0.558227i
$637$	−14.8417	−	6.98459i	−0.588048	−	0.276739i
$638$		−	4.85564i		−	0.192237i
$639$	−40.6925	−	3.46454i	−1.60977	−	0.137055i
$640$	−22.3015	+	12.8758i	−0.881544	+	0.508960i
$641$			31.0879i			1.22790i	0.789346	+	0.613949i	$0.210420\pi$
$641$			31.0879i			1.22790i	−0.789346	+	0.613949i	$0.789580\pi$
$642$	1.30076	−	1.19472i	0.0513369	−	0.0471518i
$643$	−0.977928	+	0.564607i	−0.0385657	+	0.0222659i	−0.519159	−	0.854678i	$-0.673755\pi$
$643$	−0.977928	+	0.564607i	−0.0385657	+	0.0222659i	0.480593	+	0.876944i	$0.340421\pi$
$644$	−12.7424	+	8.08627i	−0.502121	+	0.318644i
$645$	4.75591	+	21.3348i	0.187264	+	0.840057i
$646$	−1.26011	−	2.18257i	−0.0495782	−	0.0858719i
$647$	13.5992	+	23.5545i	0.534640	+	0.926023i	0.999181	+	0.0404713i	$0.0128859\pi$
$647$	13.5992	+	23.5545i	0.534640	+	0.926023i	−0.464541	+	0.885552i	$0.653781\pi$
$648$	−1.74986	+	10.2019i	−0.0687410	+	0.400769i
$649$	15.8162	+	9.13148i	0.620839	+	0.358442i
$650$	−1.50300	+	2.60328i	−0.0589526	+	0.102109i
$651$	−0.561940	+	2.09219i	−0.0220242	+	0.0819995i
$652$	24.2386	+	41.9824i	0.949256	+	1.64416i
$653$			22.2892i			0.872243i	0.899888	+	0.436121i	$0.143648\pi$
$653$			22.2892i			0.872243i	−0.899888	+	0.436121i	$0.856352\pi$
$654$	0.607159	−	0.135347i	0.0237418	−	0.00529247i
$655$	−22.8854			−0.894205
$656$	−10.9123	+	18.9007i	−0.426055	+	0.737949i
$657$	1.26011	+	2.68594i	0.0491614	+	0.104788i
$658$	−2.66128	+	1.68883i	−0.103747	+	0.0658375i
$659$	−7.69208	−	4.44103i	−0.299641	−	0.172998i	0.342641	−	0.939467i	$-0.388679\pi$
$659$	−7.69208	−	4.44103i	−0.299641	−	0.172998i	−0.642282	+	0.766469i	$0.722012\pi$
$660$	−38.5764	+	8.59937i	−1.50158	+	0.334730i
$661$	16.7724	+	9.68352i	0.652369	+	0.376645i	0.789363	−	0.613926i	$-0.210411\pi$
$661$	16.7724	+	9.68352i	0.652369	+	0.376645i	−0.136994	+	0.990572i	$0.543744\pi$
$662$	−4.84060	−	2.79472i	−0.188135	−	0.108620i
$663$	−13.3313	+	2.97179i	−0.517746	+	0.115415i
$664$	10.9434	+	6.31819i	0.424687	+	0.245193i
$665$	−17.4216	+	11.0557i	−0.675583	+	0.428721i
$666$	−6.84112	−	0.582451i	−0.265088	−	0.0225695i
$667$	−6.31999	+	10.9465i	−0.244711	+	0.423852i
$668$	3.35204			0.129694
$669$	10.8766	−	2.42458i	0.420512	−	0.0937397i
$670$		−	1.41702i		−	0.0547444i
$671$	3.11754	+	5.39973i	0.120351	+	0.208454i
$672$	3.95314	−	14.7182i	0.152496	−	0.567766i
$673$	11.5828	−	20.0620i	0.446484	−	0.773333i	−0.551670	−	0.834062i	$-0.686009\pi$
$673$	11.5828	−	20.0620i	0.446484	−	0.773333i	0.998154	+	0.0607292i	$0.0193426\pi$
$674$	−1.69310	−	0.977511i	−0.0652157	−	0.0376523i
$675$	13.8711	+	17.9469i	0.533899	+	0.690775i
$676$	−7.18476	−	12.4444i	−0.276337	−	0.478630i
$677$	1.56346	+	2.70800i	0.0600887	+	0.104077i	0.894505	−	0.447058i	$-0.147528\pi$
$677$	1.56346	+	2.70800i	0.0600887	+	0.104077i	−0.834416	+	0.551135i	$0.814195\pi$
$678$	0.240004	+	1.07665i	0.00921730	+	0.0413484i
$679$	12.8664	−	8.16496i	0.493768	−	0.313343i
$680$	10.2576	−	5.92220i	0.393359	−	0.227106i
$681$	25.1806	−	23.1279i	0.964924	−	0.886262i
$682$		−	0.541307i		−	0.0207277i
$683$	27.1966	−	15.7020i	1.04065	−	0.600819i	0.120632	−	0.992697i	$-0.461508\pi$
$683$	27.1966	−	15.7020i	1.04065	−	0.600819i	0.920017	+	0.391878i	$0.128175\pi$
$684$	6.21383	+	13.2449i	0.237592	+	0.506431i
$685$		−	37.3621i		−	1.42753i
$686$	−4.33532	+	3.29033i	−0.165523	+	0.125625i
$687$	−12.7790	−	13.9132i	−0.487549	−	0.530822i
$688$	−14.3892			−0.548585
$689$	−6.75691	+	11.7033i	−0.257418	+	0.445860i
$690$	−4.42976	−	1.39102i	−0.168638	−	0.0529553i
$691$	38.2557	−	22.0869i	1.45532	−	0.840227i	0.456540	−	0.889703i	$-0.349088\pi$
$691$	38.2557	−	22.0869i	1.45532	−	0.840227i	0.998775	+	0.0494760i	$0.0157551\pi$
$692$	−45.7868			−1.74055
$693$	16.6024	−	26.0933i	0.630673	−	0.991201i
$694$	7.83164			0.297285
$695$	35.3463	−	20.4072i	1.34076	−	0.774089i
$696$	−1.83794	−	8.24490i	−0.0696668	−	0.312522i
$697$	10.5244	−	18.2288i	0.398640	−	0.690465i
$698$	−6.96086			−0.263472
$699$	35.1266	−	7.83036i	1.32861	−	0.296171i
$700$	−11.8422	−	18.6610i	−0.447592	−	0.705320i
$701$			9.69906i			0.366328i	0.983082	+	0.183164i	$0.0586340\pi$
$701$			9.69906i			0.366328i	−0.983082	+	0.183164i	$0.941366\pi$
$702$	−3.54591	+	0.479450i	−0.133832	+	0.0180957i
$703$	−17.1876	+	9.92326i	−0.648242	+	0.374263i
$704$		−	23.3840i		−	0.881316i
$705$	20.5007	+	6.43760i	0.772103	+	0.242454i
$706$	−1.16775	+	0.674202i	−0.0439490	+	0.0253739i
$707$	−21.0324	+	40.2295i	−0.791005	+	1.51299i
$708$	14.8217	+	4.65429i	0.557035	+	0.174919i
$709$	0.548932	+	0.950778i	0.0206156	+	0.0357072i	0.876149	−	0.482040i	$-0.160104\pi$
$709$	0.548932	+	0.950778i	0.0206156	+	0.0357072i	−0.855534	+	0.517747i	$0.826771\pi$
$710$	6.12132	+	10.6024i	0.229729	+	0.397903i
$711$	25.1991	−	11.8221i	0.945040	−	0.443365i
$712$	−4.29977	−	2.48247i	−0.161141	−	0.0930346i
$713$	−0.704553	+	1.22032i	−0.0263857	+	0.0457014i
$714$	−1.17556	+	4.37680i	−0.0439942	+	0.163797i
$715$	−13.9710	−	24.1985i	−0.522486	−	0.904972i
$716$		−	48.5815i		−	1.81558i
$717$	−14.1851	+	45.1730i	−0.529753	+	1.68702i
$718$	−1.80165			−0.0672371
$719$	−11.3648	+	19.6844i	−0.423835	+	0.734103i	−0.996311	−	0.0858183i	$-0.972650\pi$
$719$	−11.3648	+	19.6844i	−0.423835	+	0.734103i	0.572476	+	0.819921i	$0.305983\pi$
$720$	−29.0016	+	13.6061i	−1.08083	+	0.507068i
$721$	−23.0241	−	12.0372i	−0.857462	−	0.448289i
$722$	3.18269	+	1.83753i	0.118448	+	0.0683858i
$723$	−24.9864	−	27.2041i	−0.929254	−	1.01173i
$724$	−37.1280	−	21.4359i	−1.37985	−	0.796658i
$725$	−16.0310	−	9.25550i	−0.595376	−	0.343741i
$726$	−0.637801	+	2.03110i	−0.0236710	+	0.0753812i
$727$	3.47919	+	2.00871i	0.129036	+	0.0744990i	0.563129	−	0.826369i	$-0.309598\pi$
$727$	3.47919	+	2.00871i	0.129036	+	0.0744990i	−0.434093	+	0.900868i	$0.642931\pi$
$728$	7.12409	−	0.298463i	0.264036	−	0.0110618i
$729$	−6.80552	+	26.1282i	−0.252056	+	0.967713i
$730$	0.444689	−	0.770224i	0.0164587	−	0.0285073i
$731$	13.8777			0.513285
$732$	3.58778	+	3.90623i	0.132608	+	0.144378i
$733$		−	8.31602i		−	0.307159i	−0.988136	−	0.153580i	$-0.950920\pi$
$733$		−	8.31602i		−	0.307159i	0.988136	−	0.153580i	$-0.0490801\pi$
$734$	3.88296	+	6.72549i	0.143323	+	0.248242i
$735$	36.2052	+	8.11620i	1.33545	+	0.299370i
$736$	4.95640	−	8.58473i	0.182695	−	0.316437i
$737$	5.31698	+	3.06976i	0.195854	+	0.113076i
$738$	3.15229	−	4.52435i	0.116037	−	0.166544i
$739$	−2.28507	−	3.95785i	−0.0840576	−	0.145592i	0.820932	−	0.571026i	$-0.193455\pi$
$739$	−2.28507	−	3.95785i	−0.0840576	−	0.145592i	−0.904989	+	0.425434i	$0.860121\pi$
$740$	−22.8040	−	39.4976i	−0.838290	−	1.45196i
$741$	−7.61759	+	6.99659i	−0.279839	+	0.257026i
$742$	2.40253	+	3.78592i	0.0881995	+	0.138986i
$743$	1.51258	−	0.873286i	0.0554910	−	0.0320378i	−0.471998	−	0.881600i	$-0.656467\pi$
$743$	1.51258	−	0.873286i	0.0554910	−	0.0320378i	0.527489	+	0.849562i	$0.323134\pi$
$744$	−0.204893	−	0.919142i	−0.00751176	−	0.0336974i
$745$			25.9312i			0.950046i
$746$	−5.11954	+	2.95577i	−0.187440	+	0.108218i
$747$	27.0446	+	18.8430i	0.989510	+	0.689430i
$748$			25.0929i			0.917486i
$749$	−7.75141	+	4.91900i	−0.283230	+	0.179736i
$750$	−0.296215	+	0.943307i	−0.0108162	+	0.0344447i
$751$	5.83293			0.212847			0.106423	−	0.994321i	$-0.466060\pi$
$751$	5.83293			0.212847			0.106423	+	0.994321i	$0.466060\pi$
$752$	−7.07260	+	12.2501i	−0.257911	+	0.446715i
$753$	−34.1081	+	31.3275i	−1.24297	+	1.14164i
$754$	2.52890	−	1.46006i	0.0920970	−	0.0531723i
$755$	−10.2719			−0.373834
$756$	8.95504	−	24.7372i	0.325692	−	0.899683i
$757$	−42.0967			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$757$	−42.0967			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$758$	4.44255	−	2.56491i	0.161361	−	0.0931617i
$759$	14.8158	−	13.6080i	0.537779	−	0.493939i
$760$	4.48466	−	7.76766i	0.162676	−	0.281763i
$761$	0.586863			0.0212738			0.0106369	−	0.999943i	$-0.496614\pi$
$761$	0.586863			0.0212738			0.0106369	+	0.999943i	$0.496614\pi$
$762$	0.419185	−	1.33491i	0.0151855	−	0.0483586i
$763$	−3.23062	+	0.135347i	−0.116956	+	0.00489988i
$764$		−	8.20750i		−	0.296937i
$765$	27.9706	−	13.1224i	1.01128	−	0.474440i
$766$	7.14208	−	4.12348i	0.258054	−	0.148987i
$767$			10.9831i			0.396577i
$768$	−3.59135	−	16.1106i	−0.129592	−	0.581342i
$769$	45.1905	−	26.0907i	1.62961	−	0.940856i	0.645403	−	0.763843i	$-0.276690\pi$
$769$	45.1905	−	26.0907i	1.62961	−	0.940856i	0.984208	−	0.177014i	$-0.0566437\pi$
$770$	−9.26306	+	0.388075i	−0.333817	+	0.0139852i
$771$	3.89426	−	3.57679i	0.140248	−	0.128815i
$772$	22.3369	+	38.6887i	0.803923	+	1.39244i
$773$	16.3906	+	28.3894i	0.589530	+	1.02110i	0.994294	+	0.106674i	$0.0340202\pi$
$773$	16.3906	+	28.3894i	0.589530	+	1.02110i	−0.404764	+	0.914421i	$0.632646\pi$
$774$	3.62249	+	0.308417i	0.130208	+	0.0110858i
$775$	−1.78714	−	1.03180i	−0.0641959	−	0.0370635i
$776$	−3.31206	+	5.73666i	−0.118896	+	0.205934i
$777$	34.4670	+	9.25747i	1.23650	+	0.332110i
$778$	5.03093	+	8.71383i	0.180368	+	0.312406i
$779$		−	15.9395i		−	0.571090i
$780$	−16.0784	−	17.5054i	−0.575698	−	0.626795i
$781$	−53.0436			−1.89805
$782$	−1.47390	+	2.55287i	−0.0527066	+	0.0912906i
$783$	−2.95246	−	21.8358i	−0.105512	−	0.780346i
$784$	−10.4005	+	22.1001i	−0.371446	+	0.789291i
$785$	−44.2821	−	25.5663i	−1.58050	−	0.912500i
$786$	−1.14037	+	3.63155i	−0.0406756	+	0.129533i
$787$	−35.5013	−	20.4967i	−1.26549	−	0.730628i	−0.291355	−	0.956615i	$-0.594106\pi$
$787$	−35.5013	−	20.4967i	−1.26549	−	0.730628i	−0.974130	+	0.225987i	$0.927439\pi$
$788$	−31.1251	−	17.9701i	−1.10879	−	0.640158i
$789$	−19.0010	−	20.6875i	−0.676453	−	0.736493i
$790$	−7.22614	−	4.17201i	−0.257095	−	0.148434i
$791$	−0.240004	−	5.72872i	−0.00853356	−	0.203690i
$792$	−1.14049	+	13.3955i	−0.0405256	+	0.475990i
$793$	−1.87485	+	3.24733i	−0.0665778	+	0.115316i
$794$	3.83195			0.135991
$795$	9.15810	−	29.1643i	0.324804	−	1.03435i
$796$		−	8.68244i		−	0.307741i
$797$	17.0441	+	29.5213i	0.603734	+	1.04570i	0.992250	+	0.124256i	$0.0396544\pi$
$797$	17.0441	+	29.5213i	0.603734	+	1.04570i	−0.388516	+	0.921442i	$0.627012\pi$
$798$	0.886249	+	3.31544i	0.0313729	+	0.117365i
$799$	6.82116	−	11.8146i	0.241315	−	0.417971i
$800$	12.5722	+	7.25854i	0.444493	+	0.256628i
$801$	−10.6261	−	7.40358i	−0.375453	−	0.261593i
$802$	−2.69672	−	4.67086i	−0.0952245	−	0.164934i
$803$	1.92670	+	3.33714i	0.0679918	+	0.117765i
$804$	4.98268	+	1.56465i	0.175725	+	0.0551809i
$805$	21.3877	+	11.1817i	0.753818	+	0.394103i
$806$	0.281922	−	0.162768i	0.00993027	−	0.00573324i
$807$	1.00225	+	0.314725i	0.0352810	+	0.0110789i
$808$		−	19.7334i		−	0.694219i
$809$	6.01547	−	3.47304i	0.211493	−	0.122105i	−0.390512	−	0.920598i	$-0.627702\pi$
$809$	6.01547	−	3.47304i	0.211493	−	0.122105i	0.602005	+	0.798492i	$0.294369\pi$
$810$	7.59277	−	2.80371i	0.266783	−	0.0985122i
$811$		−	39.8573i		−	1.39958i	−0.714350	−	0.699789i	$-0.753277\pi$
$811$		−	39.8573i		−	1.39958i	0.714350	−	0.699789i	$-0.246723\pi$
$812$	0.898690	+	21.4511i	0.0315379	+	0.752785i
$813$	−38.8364	+	8.65734i	−1.36205	+	0.303626i
$814$	−8.91756			−0.312560
$815$	38.7620	−	67.1378i	1.35777	−	2.35173i
$816$	4.42518	+	19.8512i	0.154912	+	0.694930i
$817$	9.10111	−	5.25453i	0.318408	−	0.183833i
$818$	1.90071			0.0664566
$819$	18.5820	+	0.800721i	0.649309	+	0.0279794i
$820$	36.6294			1.27915
$821$	−36.4612	+	21.0509i	−1.27250	+	0.734680i	−0.975459	−	0.220183i	$-0.929334\pi$
$821$	−36.4612	+	21.0509i	−1.27250	+	0.734680i	−0.297045	+	0.954863i	$0.596001\pi$
$822$	−5.92879	−	1.86174i	−0.206790	−	0.0649358i
$823$	−16.3411	+	28.3035i	−0.569614	+	0.986600i	0.426990	+	0.904256i	$0.359574\pi$
$823$	−16.3411	+	28.3035i	−0.569614	+	0.986600i	−0.996604	+	0.0823435i	$0.973760\pi$
$824$	11.2938			0.393438
$825$	19.9286	+	21.6974i	0.693826	+	0.755408i
$826$	3.22948	+	1.68840i	0.112368	+	0.0587470i
$827$			31.4399i			1.09327i	0.837370	+	0.546637i	$0.184092\pi$
$827$			31.4399i			1.09327i	−0.837370	+	0.546637i	$0.815908\pi$
$828$	9.78249	−	14.0404i	0.339965	−	0.487938i
$829$	35.7122	−	20.6185i	1.24034	−	0.716109i	0.271174	−	0.962530i	$-0.412588\pi$
$829$	35.7122	−	20.6185i	1.24034	−	0.716109i	0.969163	+	0.246421i	$0.0792547\pi$
$830$		−	9.88102i		−	0.342975i
$831$	−16.9449	+	15.5635i	−0.587811	+	0.539891i
$832$	12.1788	−	7.03141i	0.422222	−	0.243770i
$833$	10.0307	−	21.3145i	0.347544	−	0.738502i
$834$	−1.47701	−	6.62578i	−0.0511446	−	0.229432i
$835$	−2.68027	−	4.64236i	−0.0927546	−	0.160656i
$836$	9.50094	+	16.4561i	0.328597	+	0.569147i
$837$	−0.329140	−	2.43425i	−0.0113768	−	0.0841400i
$838$	3.62173	+	2.09100i	0.125110	+	0.0722326i
$839$	4.04385	−	7.00416i	0.139609	−	0.241810i	−0.787740	−	0.616009i	$-0.788749\pi$
$839$	4.04385	−	7.00416i	0.139609	−	0.241810i	0.927349	+	0.374198i	$0.122082\pi$
$840$	−15.5818	+	4.16517i	−0.537624	+	0.143712i
$841$	−5.50894	−	9.54177i	−0.189963	−	0.329026i
$842$			8.91707i			0.307302i
$843$	−11.0952	+	2.47332i	−0.382139	+	0.0851857i
$844$	13.1715			0.453382
$845$	−11.4898	+	19.9009i	−0.395260	+	0.684611i
$846$	2.04309	−	2.93236i	0.0702429	−	0.100817i
$847$	5.12695	−	9.80654i	0.176164	−	0.336957i
$848$	17.4269	+	10.0615i	0.598444	+	0.345512i
$849$	−5.02491	+	1.12014i	−0.172455	+	0.0384432i
$850$	−3.73863	−	2.15850i	−0.128234	−	0.0740359i
$851$	20.1037	+	11.6069i	0.689147	+	0.397879i
$852$	−44.0404	+	9.81740i	−1.50880	+	0.336338i
$853$	24.5887	+	14.1963i	0.841900	+	0.486071i	0.857910	−	0.513801i	$-0.171763\pi$
$853$	24.5887	+	14.1963i	0.841900	+	0.486071i	−0.0160098	+	0.999872i	$0.505096\pi$
$854$	0.666631	+	1.05048i	0.0228117	+	0.0359468i
$855$	13.3748	−	19.1963i	0.457408	−	0.656499i
$856$	1.99536	−	3.45606i	0.0682000	−	0.118126i
$857$	−51.3174			−1.75297			−0.876485	−	0.481429i	$-0.840118\pi$
$857$	−51.3174			−1.75297			−0.876485	+	0.481429i	$0.840118\pi$
$858$	−4.53609	+	1.01118i	−0.154860	+	0.0345210i
$859$			16.7702i			0.572191i	0.958201	+	0.286096i	$0.0923575\pi$
$859$			16.7702i			0.572191i	−0.958201	+	0.286096i	$0.907642\pi$
$860$	12.0751	+	20.9146i	0.411756	+	0.713183i
$861$	−20.2798	+	20.2556i	−0.691133	+	0.690308i
$862$	−0.360816	+	0.624951i	−0.0122894	+	0.0212859i
$863$	14.2380	+	8.22033i	0.484668	+	0.279823i	0.722360	−	0.691517i	$-0.243057\pi$
$863$	14.2380	+	8.22033i	0.484668	+	0.279823i	−0.237692	+	0.971341i	$0.576391\pi$
$864$	2.31544	+	17.1245i	0.0787728	+	0.582587i
$865$	36.6109	+	63.4119i	1.24481	+	2.15607i
$866$	1.83000	+	3.16965i	0.0621859	+	0.107709i
$867$	2.13868	+	9.59401i	0.0726333	+	0.325830i
$868$	0.100186	+	2.39137i	0.00340054	+	0.0811683i
$869$	31.3086	−	18.0760i	1.06207	−	0.613188i
$870$	−4.86476	+	4.46818i	−0.164931	+	0.151485i
$871$			3.69223i			0.125106i
$872$	1.21726	−	0.702787i	0.0412217	−	0.0237994i
$873$	−9.87770	+	14.1770i	−0.334309	+	0.479820i
$874$			2.23226i			0.0755074i
$875$	2.38112	−	4.55447i	0.0804965	−	0.153969i
$876$	2.21732	+	2.41413i	0.0749164	+	0.0815657i
$877$	6.12350			0.206776			0.103388	−	0.994641i	$-0.467032\pi$
$877$	6.12350			0.206776			0.103388	+	0.994641i	$0.467032\pi$
$878$	2.57577	−	4.46137i	0.0869281	−	0.150564i
$879$	10.0170	+	3.14551i	0.337864	+	0.106095i
$880$	−36.0330	+	20.8037i	−1.21467	+	0.701292i
$881$	−41.3283			−1.39238			−0.696192	−	0.717855i	$-0.745124\pi$
$881$	−41.3283			−1.39238			−0.696192	+	0.717855i	$0.745124\pi$
$882$	3.09201	−	5.34078i	0.104113	−	0.179833i
$883$	24.2918			0.817483			0.408741	−	0.912650i	$-0.365968\pi$
$883$	24.2918			0.817483			0.408741	+	0.912650i	$0.365968\pi$
$884$	−13.0688	+	7.54526i	−0.439550	+	0.253775i
$885$	−5.40548	−	24.2487i	−0.181703	−	0.815111i
$886$	−1.32310	+	2.29167i	−0.0444502	+	0.0769901i
$887$	6.70071			0.224988			0.112494	−	0.993652i	$-0.464116\pi$
$887$	6.70071			0.224988			0.112494	+	0.993652i	$0.464116\pi$
$888$	−15.1421	+	3.37544i	−0.508134	+	0.113272i
$889$	−3.36961	+	6.44520i	−0.113013	+	0.216165i
$890$			3.88234i			0.130136i
$891$	−5.92843	+	34.5635i	−0.198610	+	1.15792i
$892$	10.6624	−	6.15591i	0.357002	−	0.206115i
$893$		−	10.3308i		−	0.345708i
$894$	4.11488	+	1.29214i	0.137622	+	0.0432158i
$895$	−67.2823	+	38.8455i	−2.24900	+	1.29846i
$896$	−0.931908	−	22.2440i	−0.0311329	−	0.743118i
$897$	11.5423	+	3.62448i	0.385385	+	0.121018i
$898$	4.52735	+	7.84160i	0.151080	+	0.261678i
$899$	1.00232	+	1.73608i	0.0334294	+	0.0579014i
$900$	20.5619	+	14.3263i	0.685396	+	0.477542i
$901$	−16.8074	−	9.70376i	−0.559936	−	0.323279i
$902$	3.58101	−	6.20249i	0.119235	−	0.206520i
$903$	−18.2509	−	4.90198i	−0.607350	−	0.163128i
$904$	1.24622	+	2.15852i	0.0414487	+	0.0717912i
$905$			68.5600i			2.27901i
$906$	−0.511847	+	1.62999i	−0.0170050	+	0.0541529i
$907$	20.2988			0.674010			0.337005	−	0.941503i	$-0.390586\pi$
$907$	20.2988			0.674010			0.337005	+	0.941503i	$0.390586\pi$
$908$	18.8873	−	32.7138i	0.626798	−	1.08565i
$909$	4.36668	−	51.2884i	0.144834	−	1.70113i
$910$	−2.98746	−	4.70766i	−0.0990332	−	0.156057i
$911$	−30.3982	−	17.5504i	−1.00714	−	0.581472i	−0.0967861	−	0.995305i	$-0.530856\pi$
$911$	−30.3982	−	17.5504i	−1.00714	−	0.581472i	−0.910353	+	0.413833i	$0.864190\pi$
$912$	10.4183	+	11.3431i	0.344986	+	0.375606i
$913$	37.0757	+	21.4057i	1.22703	+	0.708425i
$914$	3.51936	+	2.03190i	0.116410	+	0.0672093i
$915$	2.54111	−	8.09225i	0.0840064	−	0.267521i
$916$	−18.0756	−	10.4359i	−0.597233	−	0.344813i
$917$	9.16685	−	17.5338i	0.302716	−	0.579018i
$918$	−0.688551	−	5.09237i	−0.0227256	−	0.168073i
$919$	−16.9132	+	29.2946i	−0.557916	+	0.966339i	0.439754	+	0.898118i	$0.355066\pi$
$919$	−16.9132	+	29.2946i	−0.557916	+	0.966339i	−0.997670	+	0.0682206i	$0.978268\pi$
$920$	−10.4911			−0.345882
$921$	−25.3110	−	27.5576i	−0.834027	−	0.908053i
$922$		−	3.62629i		−	0.119425i
$923$	−15.9499	−	27.6260i	−0.524996	−	0.909320i
$924$	8.86349	−	33.0002i	0.291587	−	1.08563i
$925$	−16.9981	+	29.4415i	−0.558893	+	0.968031i
$926$	−3.24639	−	1.87431i	−0.106683	−	0.0615935i
$927$	29.3533	+	2.49913i	0.964089	+	0.0820823i
$928$	−7.05115	−	12.2130i	−0.231465	−	0.400910i
$929$	16.0586	+	27.8142i	0.526864	+	0.912555i	0.999510	+	0.0313029i	$0.00996565\pi$
$929$	16.0586	+	27.8142i	0.526864	+	0.912555i	−0.472646	+	0.881252i	$0.656701\pi$
$930$	−0.542324	+	0.498113i	−0.0177835	+	0.0163338i
$931$	−1.49208	−	17.7762i	−0.0489009	−	0.582590i
$932$	34.4348	−	19.8810i	1.12795	−	0.651222i
$933$	4.15423	+	18.6357i	0.136004	+	0.610105i
$934$			3.22668i			0.105580i
$935$	34.7520	−	20.0641i	1.13651	−	0.656166i
$936$	−7.31955	+	3.43396i	−0.239247	+	0.112243i
$937$			13.9224i			0.454824i	0.973799	+	0.227412i	$0.0730263\pi$
$937$			13.9224i			0.454824i	−0.973799	+	0.227412i	$0.926974\pi$
$938$	1.08567	+	0.567596i	0.0354482	+	0.0185327i
$939$	7.03343	−	22.3982i	0.229527	−	0.730938i
$940$	23.7405			0.774331
$941$	28.6047	−	49.5448i	0.932487	−	1.61512i	0.153433	−	0.988159i	$-0.450967\pi$
$941$	28.6047	−	49.5448i	0.932487	−	1.61512i	0.779054	−	0.626956i	$-0.215700\pi$
$942$	−6.26353	+	5.75292i	−0.204077	+	0.187440i
$943$	−16.1460	+	9.32192i	−0.525787	+	0.303563i
$944$	16.3545			0.532294
$945$	−41.4199	+	7.37754i	−1.34739	+	0.239991i
$946$	4.72200			0.153525
$947$	29.8658	−	17.2430i	0.970509	−	0.560324i	0.0711175	−	0.997468i	$-0.477343\pi$
$947$	29.8658	−	17.2430i	0.970509	−	0.560324i	0.899391	+	0.437144i	$0.144010\pi$
$948$	22.6490	−	20.8026i	0.735605	−	0.675637i
$949$	−1.15869	+	2.00691i	−0.0376128	+	0.0651472i
$950$	−3.26910			−0.106064
$951$	5.78802	−	18.4321i	0.187689	−	0.597703i
$952$	0.428630	+	10.2311i	0.0138920	+	0.331591i
$953$		−	2.58761i		−	0.0838209i	−0.999121	−	0.0419104i	$-0.986656\pi$
$953$		−	2.58761i		−	0.0838209i	0.999121	−	0.0419104i	$-0.0133444\pi$
$954$	−4.17157	−	2.90649i	−0.135060	−	0.0941012i
$955$	−11.3669	+	6.56267i	−0.367824	+	0.212363i
$956$			52.3119i			1.69189i
$957$	−6.22683	−	27.9333i	−0.201285	−	0.902954i
$958$	2.84900	−	1.64487i	0.0920470	−	0.0531434i
$959$	28.6253	+	14.9656i	0.924360	+	0.483264i
$960$	−23.4279	+	21.5180i	−0.756132	+	0.694491i
$961$	−15.3883	−	26.6532i	−0.496396	−	0.859782i
$962$	−2.68145	−	4.64441i	−0.0864535	−	0.149742i
$963$	5.95084	−	8.54100i	0.191763	−	0.275230i
$964$	−35.3426	−	20.4051i	−1.13831	−	0.657203i
$965$	35.7209	−	61.8704i	1.14990	−	1.99168i
$966$	2.84010	−	2.83672i	0.0913789	−	0.0912698i
$967$	2.79472	+	4.84059i	0.0898721	+	0.155663i	0.907457	−	0.420145i	$-0.138021\pi$
$967$	2.79472	+	4.84059i	0.0898721	+	0.155663i	−0.817585	+	0.575808i	$0.804688\pi$
$968$			4.81030i			0.154609i
$969$	−10.0480	−	10.9398i	−0.322787	−	0.351437i
$970$	5.17973			0.166311
$971$	−8.01661	+	13.8852i	−0.257265	+	0.445597i	−0.965508	−	0.260372i	$-0.916155\pi$
$971$	−8.01661	+	13.8852i	−0.257265	+	0.445597i	0.708243	+	0.705969i	$0.249488\pi$
$972$	1.47489	+	29.7942i	0.0473071	+	0.955650i
$973$	1.47701	+	35.2551i	0.0473507	+	1.13023i
$974$	0.755007	+	0.435904i	0.0241920	+	0.0139673i
$975$	−5.30797	+	16.9034i	−0.169991	+	0.541343i
$976$	4.83547	+	2.79176i	0.154780	+	0.0893621i
$977$	−38.0208	−	21.9513i	−1.21639	−	0.702285i	−0.252248	−	0.967663i	$-0.581170\pi$
$977$	−38.0208	−	21.9513i	−1.21639	−	0.702285i	−0.964144	+	0.265378i	$0.914503\pi$
$978$	−8.72222	−	9.49638i	−0.278906	−	0.303661i
$979$	−14.5674	−	8.41048i	−0.465576	−	0.268800i
$980$	40.8502	−	3.42884i	1.30491	−	0.109530i
$981$	3.31926	−	1.55723i	0.105976	−	0.0497185i
$982$	3.42377	−	5.93015i	0.109257	−	0.189239i
$983$	−18.1762			−0.579730			−0.289865	−	0.957068i	$-0.593610\pi$
$983$	−18.1762			−0.579730			−0.289865	+	0.957068i	$0.593610\pi$
$984$	3.73283	−	11.8873i	0.118998	−	0.378954i
$985$			57.4751i			1.83131i
$986$	2.09683	+	3.63181i	0.0667766	+	0.115660i
$987$	−13.1439	+	13.1282i	−0.418375	+	0.417876i
$988$	−5.71374	+	9.89649i	−0.181778	+	0.314849i
$989$	−10.6453	−	6.14604i	−0.338499	−	0.195433i
$990$	9.51720	−	4.46499i	0.302477	−	0.141907i
$991$	−23.8146	−	41.2481i	−0.756496	−	1.31029i	−0.944627	−	0.328145i	$-0.893576\pi$
$991$	−23.8146	−	41.2481i	−0.756496	−	1.31029i	0.188131	−	0.982144i	$-0.439757\pi$
$992$	−0.786063	−	1.36150i	−0.0249575	−	0.0432277i
$993$	−31.4307	−	9.86979i	−0.997423	−	0.313208i
$994$	−10.5751	+	0.443042i	−0.335421	+	0.0140524i
$995$	−12.0246	+	6.94242i	−0.381206	+	0.220090i
$996$	34.7446	+	10.9104i	1.10092	+	0.345710i
$997$		−	32.8902i		−	1.04164i	−0.853666	−	0.520822i	$-0.825626\pi$
$997$		−	32.8902i		−	1.04164i	0.853666	−	0.520822i	$-0.174374\pi$
$998$	1.16711	−	0.673830i	0.0369442	−	0.0213297i
$999$	−40.1022	+	5.42230i	−1.26878	+	0.171554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.s.b.47.3	yes	10
3.2	odd	2		189.2.s.b.89.3		10
4.3	odd	2		1008.2.df.b.929.5		10
7.2	even	3		441.2.o.c.146.3		10
7.3	odd	6		63.2.i.b.38.3	yes	10
7.4	even	3		441.2.i.b.227.3		10
7.5	odd	6		441.2.o.d.146.3		10
7.6	odd	2		441.2.s.b.362.3		10
9.2	odd	6		567.2.p.d.404.3		10
9.4	even	3		189.2.i.b.152.3		10
9.5	odd	6		63.2.i.b.5.3	✓	10
9.7	even	3		567.2.p.c.404.3		10
12.11	even	2		3024.2.df.b.1601.1		10
21.2	odd	6		1323.2.o.d.440.3		10
21.5	even	6		1323.2.o.c.440.3		10
21.11	odd	6		1323.2.i.b.521.3		10
21.17	even	6		189.2.i.b.143.3		10
21.20	even	2		1323.2.s.b.656.3		10
28.3	even	6		1008.2.ca.b.353.4		10
36.23	even	6		1008.2.ca.b.257.4		10
36.31	odd	6		3024.2.ca.b.2609.1		10
63.4	even	3		1323.2.s.b.962.3		10
63.5	even	6		441.2.o.c.293.3		10
63.13	odd	6		1323.2.i.b.1097.3		10
63.23	odd	6		441.2.o.d.293.3		10
63.31	odd	6		189.2.s.b.17.3		10
63.32	odd	6		441.2.s.b.374.3		10
63.38	even	6		567.2.p.c.80.3		10
63.40	odd	6		1323.2.o.d.881.3		10
63.41	even	6		441.2.i.b.68.3		10
63.52	odd	6		567.2.p.d.80.3		10
63.58	even	3		1323.2.o.c.881.3		10
63.59	even	6	inner	63.2.s.b.59.3	yes	10
84.59	odd	6		3024.2.ca.b.2033.1		10
252.31	even	6		3024.2.df.b.17.1		10
252.59	odd	6		1008.2.df.b.689.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.3	✓	10	9.5	odd	6
63.2.i.b.38.3	yes	10	7.3	odd	6
63.2.s.b.47.3	yes	10	1.1	even	1	trivial
63.2.s.b.59.3	yes	10	63.59	even	6	inner
189.2.i.b.143.3		10	21.17	even	6
189.2.i.b.152.3		10	9.4	even	3
189.2.s.b.17.3		10	63.31	odd	6
189.2.s.b.89.3		10	3.2	odd	2
441.2.i.b.68.3		10	63.41	even	6
441.2.i.b.227.3		10	7.4	even	3
441.2.o.c.146.3		10	7.2	even	3
441.2.o.c.293.3		10	63.5	even	6
441.2.o.d.146.3		10	7.5	odd	6
441.2.o.d.293.3		10	63.23	odd	6
441.2.s.b.362.3		10	7.6	odd	2
441.2.s.b.374.3		10	63.32	odd	6
567.2.p.c.80.3		10	63.38	even	6
567.2.p.c.404.3		10	9.7	even	3
567.2.p.d.80.3		10	63.52	odd	6
567.2.p.d.404.3		10	9.2	odd	6
1008.2.ca.b.257.4		10	36.23	even	6
1008.2.ca.b.353.4		10	28.3	even	6
1008.2.df.b.689.5		10	252.59	odd	6
1008.2.df.b.929.5		10	4.3	odd	2
1323.2.i.b.521.3		10	21.11	odd	6
1323.2.i.b.1097.3		10	63.13	odd	6
1323.2.o.c.440.3		10	21.5	even	6
1323.2.o.c.881.3		10	63.58	even	3
1323.2.o.d.440.3		10	21.2	odd	6
1323.2.o.d.881.3		10	63.40	odd	6
1323.2.s.b.656.3		10	21.20	even	2
1323.2.s.b.962.3		10	63.4	even	3
3024.2.ca.b.2033.1		10	84.59	odd	6
3024.2.ca.b.2609.1		10	36.31	odd	6
3024.2.df.b.17.1		10	252.31	even	6
3024.2.df.b.1601.1		10	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.254498 + 0.146935i) q^{2} +(-1.27564 + 1.17164i) q^{3} +(-0.956820 + 1.65726i) q^{4} +3.06027 q^{5} +(0.152492 - 0.485617i) q^{6} +(-1.22581 + 2.34465i) q^{7} -1.15010i q^{8} +(0.254498 - 2.98919i) q^{9} +O(q^{10})\)	\(q+(-0.254498 + 0.146935i) q^{2} +(-1.27564 + 1.17164i) q^{3} +(-0.956820 + 1.65726i) q^{4} +3.06027 q^{5} +(0.152492 - 0.485617i) q^{6} +(-1.22581 + 2.34465i) q^{7} -1.15010i q^{8} +(0.254498 - 2.98919i) q^{9} +(-0.778834 + 0.449660i) q^{10} -3.89647i q^{11} +(-0.721166 - 3.23512i) q^{12} +(2.02935 - 1.17164i) q^{13} +(-0.0325450 - 0.776824i) q^{14} +(-3.90379 + 3.58555i) q^{15} +(-1.74465 - 3.02182i) q^{16} +(1.68263 + 2.91440i) q^{17} +(0.374446 + 0.798138i) q^{18} +(2.20696 + 1.27419i) q^{19} +(-2.92813 + 5.07167i) q^{20} +(-1.18341 - 4.42714i) q^{21} +(0.572527 + 0.991647i) q^{22} -2.98075i q^{23} +(1.34751 + 1.46711i) q^{24} +4.36525 q^{25} +(-0.344311 + 0.596363i) q^{26} +(3.17762 + 4.11130i) q^{27} +(-2.71283 - 4.27489i) q^{28} +(-3.67241 - 2.12027i) q^{29} +(0.466668 - 1.48612i) q^{30} +(-0.409400 - 0.236367i) q^{31} +(2.88005 + 1.66280i) q^{32} +(4.56528 + 4.97049i) q^{33} +(-0.856452 - 0.494473i) q^{34} +(-3.75130 + 7.17527i) q^{35} +(4.71035 + 3.28188i) q^{36} +(-3.89395 + 6.74451i) q^{37} -0.748891 q^{38} +(-1.21596 + 3.87227i) q^{39} -3.51962i q^{40} +(-3.12737 - 5.41676i) q^{41} +(0.951677 + 0.952814i) q^{42} +(2.06191 - 3.57133i) q^{43} +(6.45748 + 3.72823i) q^{44} +(0.778834 - 9.14772i) q^{45} +(0.437976 + 0.758597i) q^{46} +(-2.02694 - 3.51076i) q^{47} +(5.76605 + 1.81064i) q^{48} +(-3.99479 - 5.74818i) q^{49} +(-1.11095 + 0.641408i) q^{50} +(-5.56106 - 1.74627i) q^{51} +4.48421i q^{52} +(-4.99439 + 2.88351i) q^{53} +(-1.41279 - 0.579416i) q^{54} -11.9243i q^{55} +(2.69658 + 1.40980i) q^{56} +(-4.30818 + 0.960372i) q^{57} +1.24616 q^{58} +(-2.34352 + 4.05910i) q^{59} +(-2.20696 - 9.90033i) q^{60} +(-1.38580 + 0.800092i) q^{61} +0.138922 q^{62} +(6.69664 + 4.26088i) q^{63} +6.00131 q^{64} +(6.21035 - 3.58555i) q^{65} +(-1.89219 - 0.594182i) q^{66} +(-0.787831 + 1.36456i) q^{67} -6.43989 q^{68} +(3.49238 + 3.80236i) q^{69} +(-0.0995964 - 2.37729i) q^{70} -13.6132i q^{71} +(-3.43786 - 0.292699i) q^{72} +(-0.856452 + 0.494473i) q^{73} -2.28862i q^{74} +(-5.56848 + 5.11453i) q^{75} +(-4.22333 + 2.43834i) q^{76} +(9.13588 + 4.77633i) q^{77} +(-0.259511 - 1.16415i) q^{78} +(4.63908 + 8.03512i) q^{79} +(-5.33910 - 9.24760i) q^{80} +(-8.87046 - 1.52149i) q^{81} +(1.59182 + 0.919038i) q^{82} +(-5.49361 + 9.51520i) q^{83} +(8.46924 + 2.27475i) q^{84} +(5.14930 + 8.91884i) q^{85} +1.21186i q^{86} +(7.16886 - 1.59807i) q^{87} -4.48133 q^{88} +(2.15849 - 3.73861i) q^{89} +(1.14591 + 2.44252i) q^{90} +(0.259511 + 6.19433i) q^{91} +(4.93989 + 2.85205i) q^{92} +(0.799185 - 0.178153i) q^{93} +(1.03171 + 0.595655i) q^{94} +(6.75390 + 3.89937i) q^{95} +(-5.62211 + 1.25327i) q^{96} +(-4.98797 - 2.87980i) q^{97} +(1.86128 + 0.875930i) q^{98} +(-11.6473 - 0.991647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7}+O(q^{10}) \) 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7	\( 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7} - 15 q^{10} + 6 q^{13} - 6 q^{14} - 3 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} + 3 q^{19} - 3 q^{20} + 18 q^{21} + 5 q^{22} + 27 q^{24} - 14 q^{25} + 3 q^{26} + 27 q^{27} + 2 q^{28} - 15 q^{29} - 9 q^{31} + 48 q^{32} - 9 q^{33} + 3 q^{34} - 15 q^{35} - 18 q^{36} + 6 q^{37} + 36 q^{38} + 12 q^{39} - 9 q^{41} - 6 q^{42} + 3 q^{43} + 24 q^{44} + 15 q^{45} - 13 q^{46} + 15 q^{47} - 15 q^{48} - 23 q^{49} + 3 q^{50} - 24 q^{51} - 9 q^{53} + 27 q^{54} - 51 q^{56} - 36 q^{57} - 16 q^{58} - 18 q^{59} - 3 q^{60} + 12 q^{61} + 12 q^{62} + 9 q^{63} + 6 q^{64} - 3 q^{65} - 33 q^{66} - 10 q^{67} - 54 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{72} + 3 q^{73} - 21 q^{75} + 9 q^{76} + 45 q^{77} + 24 q^{78} + 20 q^{79} - 30 q^{80} - 48 q^{81} + 9 q^{82} - 15 q^{83} + 60 q^{84} + 18 q^{85} + 30 q^{87} + 16 q^{88} + 24 q^{89} + 24 q^{90} - 24 q^{91} + 39 q^{92} + 6 q^{93} - 3 q^{94} + 3 q^{96} + 6 q^{97} + 45 q^{98} + 21 q^{99}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7 - 15 * q^10 + 6 * q^13 - 6 * q^14 - 3 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 + 3 * q^19 - 3 * q^20 + 18 * q^21 + 5 * q^22 + 27 * q^24 - 14 * q^25 + 3 * q^26 + 27 * q^27 + 2 * q^28 - 15 * q^29 - 9 * q^31 + 48 * q^32 - 9 * q^33 + 3 * q^34 - 15 * q^35 - 18 * q^36 + 6 * q^37 + 36 * q^38 + 12 * q^39 - 9 * q^41 - 6 * q^42 + 3 * q^43 + 24 * q^44 + 15 * q^45 - 13 * q^46 + 15 * q^47 - 15 * q^48 - 23 * q^49 + 3 * q^50 - 24 * q^51 - 9 * q^53 + 27 * q^54 - 51 * q^56 - 36 * q^57 - 16 * q^58 - 18 * q^59 - 3 * q^60 + 12 * q^61 + 12 * q^62 + 9 * q^63 + 6 * q^64 - 3 * q^65 - 33 * q^66 - 10 * q^67 - 54 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^72 + 3 * q^73 - 21 * q^75 + 9 * q^76 + 45 * q^77 + 24 * q^78 + 20 * q^79 - 30 * q^80 - 48 * q^81 + 9 * q^82 - 15 * q^83 + 60 * q^84 + 18 * q^85 + 30 * q^87 + 16 * q^88 + 24 * q^89 + 24 * q^90 - 24 * q^91 + 39 * q^92 + 6 * q^93 - 3 * q^94 + 3 * q^96 + 6 * q^97 + 45 * q^98 + 21 * q^99

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